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THE  INTERNATIONAL  SCIENTIFIC  SERIES. 
VOLUME  XLVII. 


THE 

INTERNATIONAL  SCIENTIFIC  SERIES. 


Even    BOOK  COMPLETE    IN   OnE   VoLUME,   12mO,   AND    BOUND   IN 

Cloth. 


I.  FORMS  OF  WATEE:  a  Familiar  Exposition  of  the  Origin  and 
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New  York :  D.  APPLETON  &  CO.,  1,  3,  &  5  Bond  Street. 


THE  INTERNATIONAL  SCIENTIFIC  SERIES. 


FALLACIES. 


A  VIEW  OF  LOGIC  FROM  THE  PRACTICAL  SIDE. 


BY 


ALFRED  JJDGWICK, 

B.  A.  OXON., 
BKBKKLET  FELLOW  OF  THE  OWENS  COLLEGE,  MANCHE8TEB. 


NEW  YORK: 
D.    APPLETON    AND    COMPANY, 

1,  8,  AND  5  BOND  STREET. 

1884. 


"Be 

ns-  57590 


UNTVERSTTY  OF  CALIFORNIA 
SAKTA  BARBARA.  COLLEGE  LIBRARY 


PREFACE. 


This  book  is  intended,  like  the  others  in  the  Inter- 
national Scientific  Series,  mainly  for  the  general  reader. 
That  is  to  say,  it  requires  no  previous  technical  train- 
ing, and  is  written  as  much  as  possible  from  the  unpro- 
fessional point  of  view. 

Although  any  treatment  of  Fallacies  must  be  to  a 
great  extent  a  treatment  of  methods  of  Proof,  and  must 
therefore  demand  a  certain  amount  of  general  logical 
theory,  yet  by  trying  to  keep  chiefly  in  view  the  practical 
side  of  the  science  of  Logic, — subordinating  to  that  all 
other  interests  or  inquiries, — I  have  been  able  to  neglect 
the  discussion  of  much  debatable  matter  and  to  avoid 
definite  adherence  to  a  school.  No  doubt,  Mill  and  Bain, 
— and,  more  remotely,  Hume, — are  the  authors  to  whom 
the  general  substance  of  the  present  work  is  mainly 
traceable ;  but  one  may,  I  hope,  utilise  many  of  their 
results  without  being  compelled  to  accept  the  whole  of 
their  Philosophy.      As  regards  later  writers,  although 


VI  PREFACE. 

hints  have  here  and  there  been  taken  from  various  other 
sources,  English  and  German,  the  aid  so  obtained  has 
been,  I  think  (except  where  expressly  mentioned),  frag- 
mentary or  indirect. 

It  is  impossible  fully  to  acknowledge  all  the  viva  voce 
help  received  from  friends,  but  I  may  at  least  here 
express  my  gratitude  to  the  anonymous  Founder  of  the 
Berkeley  Fellowships  at  the  Owens  College.  The  election 
to  one  of  these,  in  1881,  has  given  me  the  opportunity  of 
finishing  this  book  (then  already  designed  for  this  Series) : 
and  has  also  provided  me  with  the  invaluable  advice  and 
criticism  of  Prof  Adamson. 

By  the  courtesy  of  the  Editor  of  Mind,  a  portion  of 
chapters  iii.  and  iv,  (Part  I.)  is  reprinted  from  that 
Journal 

Mancbesteb,  May,  1883. 


CONTENTS. 


INTRODUCTION. 

SECTION  PAGE 

I.  Difficulties  of  Treatment     ...         ...         ...         .,,         ...         ...  1 

IL  The  Practical  Side  of  Logic 11 

III.  Outline  of  the  Work           20 


PART  I. 

PEOOP   IN   GENERAL. 
CHAPTER  I. 

THE  MEANING  AND  AIMS  OF  PROOF. 
I.  Proof  and  Inference      ...         ...         ...         ...         ...         ...       81 

Importance  of  thedistinction,  31.  Amblf^uities  of  '  Inference,' 
♦Reasoning,'  etc.,  32-34.  The  problem  of  Proof  always 
narrower  than  that  of  Inference,  35. 

IT.  Proving  and  Testing      35 

Further  ambiguities  of  '  Proof,'  35-37.  Its  etymological 
meaning,  36.  Successful  resistance  to  attack,  37,  38. 
'  Practically '  sufficient  Proof,  38.  Value  of  hostile  criti- 
cism, 39.     The  discarding  of  rival  theories,  40. 


vm  CONTENTS. 


CHAPTER   IL 

TIIE  SUBJECT-MATTER  OF  PROOF:  IN  GENERAL. 
SECTION  PAGE 

I.  Beal  and  Unreal  Propositions 41 

A  thesis,  what,  41.  '  Verbal '  and  '  Unreal,'  42.  Tautology, 
43, 44.  Self-contradiction,  44-47.  '  Ultimate  beliefs '  and 
Unreality,  46.  Meaningless  terms,  47,  48.  Propositions 
apparently,  not  actually,  unreal,  48-51. 

II.  Subject  and  Phedicate  51 

'  Things  spoken  of,'  51,  52.  Propositions  viewed  as  stating 
tk  relation,  53-56.  Copula,  54.  Starting-point  and  goal  of 
an  assertion,  54,  55. 

III.  Simple  and  Complex  Peopositions     ,        ...      56 

No  sharp  line  to  be  drawn  between  them,  56.  An  argu. 
ment,  as  a  whole,  is  a  complex  proposition,  58. 


CHAPTER  III. 

THE  SUBJECT-MATTER  OF  PROOF:  MAIN  KINDS  OF  THESIS. 

I.  Indication 59 

All  propositions  assert '  indication,'  59.  Indication  and  im- 
plication, 60.    Special  sense  of  the  name,  61,  62. 

II.  Atfibmation  and  Denial  64 

III.  Abstract  and  Concrete  Propositions  66 

The  abstract  proposition,  66.  The  concrete  proposition, 
67, 71.  Exceptive  denial,  and  the  assertion  of  difference, 
68, 70.  Concrete  denials,  71.  Abstraction  and  abstract 
names,  72.  Categorical  and  hypothetical  propositions, 
73.  Respective  functions  of  abstract  and  concrete  pro- 
positions, 74 ;  their  interaction,  75-77.  *  Overtones '  in 
a  concrete  proposition,  77. 


CONTENTS.  IX 


PAOB 


SECTIOW 

IV.  Succession  and  Co-existence 78 

*  Plurality  *  of  causes,  and  their  liability  to  counteraction, 
80.  Indication  seldom  absolute,  80-82.  'Chance,' 
*  Tendency,'  and  *  Law,'  81.     Laws  incompletely  true,  82. 


CIIAPTEK   IV. 

THE  LAW  OF  COUNTER-INDICATION        84 

The  pons  asinorum  of  Logic,  84.  '  Presence,'  and  '  absence,* 
as  sign  and  signified,  85.  Statement  of  the  law,  86. 
Table  illustrating  the  same,  87.  Examples,  87-89.  Value 
of  the  law,  89-93.  The  disjunctive  proposition,  92,  Ap- 
plication of  the  law  to  concrete  propositions,  95.  One 
precaution  necessary,  96. 


CHAPTER  V. 
THE  PROCESS  OF  PROOF,  IN  GENERAL. 

L  The  Eelation  between  Thesis  and  Eeason  99 

Reason  indicates  Thesis,  100.  Material  truth  of  the  Reason, 
101.     Formal  adequacy  of  the  Reason,  102. 

IL  Consistency  103 

Principles  and  their  '  logical  outcome,*  103.  Extension  to 
analogous  cases,  104.  The  Maxims  of  Consistency, 
105-107.  The  use  of  names,  107-109.  The  generic  and 
differential  elements  in  the  meaning  of  a  name,  108. 
Analogical  and  deductive  consistency,  110. 

III.  Formal  Adequacy  in  Generai.  Ill 

The  '  Reason  given,'  and  the  whole  '  rationalisation '  of  a 
thesis,  111.  All  rationalisation  may  be  expressed  syllo- 
gistically.  111.  Proof  the  counterpart  of  Explanation, 
111,  112.  The  Principle  and  the  Application,  113.  Value 
of  the  Syllogism,  113,  114. 


X  CONTENTS. 

PAET  II. 

THE   POSSIBILITIES   OF  EEROR. 

SECTION  I.— BEFORE  PROOF. 

CHAPTER  I. 

PAGE 

INTRODUCTORY  117 

CHAPTER  II. 

THE  KINDS  OF  UNREAL  ASSERTION. 
SECTION 

I.  Tautology,  or  Platitude  120 

Causes  and  results,  120-122.  Tautologies  sometimes  useful 
as  Postulates,  122.  Common  forms  of  Tautology,  123. 
Finer  shades,  124-127.  '  The '  meaning  of  a  word,  124. 
Bain's  view  of  verbality  examined,  125,  126.  The  special 
definition,  127.  The  right  to  require  explanations  is 
practically  limited,  128. 

II.    SELF-CONTRADICTION  129 

Causes  somewhat  different  from  those  of  Tautology,  129. 
'  Bulls '  and  epigrams,  129.  Interval  between  inconsistent 
assertions,  130,  131.  The  more  dangerous  forms,  131. 
The  Sorites  difiSculty,  133-136.  Occasional  value  of  vague 
assertions,  137. 

III.  Meaningless  Term  138 

Self-contradiction  within  a  term,  138-140.  Belief  in 
mysteries,  140.  Limits  to  power  of  defining,  141.  Sum- 
mum  genus,  141.  Indefinable  terms,  143.  Ignotum  per 
ignotit'^,  142. 

IV.  Unreal  Assertion  :    Concluded  „,        ,. 143 

Recapitulation,  143,  144.  Verbal  questions,  144-146.  De- 
grees of  '  reality,'  146. 


CONTENTS.  XI 


CHAPTER  III. 

PAGE 

THE  BURDEN  OF  PROOF       148 


The  objection  'no  evidence,'  148.  Self-evident  truths, 
149,  150.  The  frustration  of  disproof,  150.  Distinction 
between  denial  and  doubt,  150,  The  simple  rule,  150, 151. 
Its  extreme  cases,  151-154.  The  sceptical  position,  153. 
The  stifling  of  inquiry,  154.  Whately's  doctrine  examined, 
154-156.  How  far  bound  to  explain  away  facts  ?  157,  158. 
The  doctrine  of  '  fair  presumptions,'  158-161.  Treatment 
of  conflicting  facts  and  awkward  questions,  161,  162. 
Artificial  and  natui-al  laws  of  discussion,  163.  Provisional 
theories,  164.  Presumption  of  weakness,  165-167.  The 
need  and  the  demand  for  Proof,  165.  Causes  of  absence 
of  Proof,  166. 


SECTION  II.—NON  SEQUITUB. 
CHAPTER  IV. 

INTRODUCTORY  168 

Nov,  sequitur  co-extensive  with  failure  in  formal  adequacy  of 
the  Beason,  168.  A  compromise  required  between  Method 
and  Guesswork  in  detecting  fallacies,  169-173.  Four 
meanings  of  'Fallacy/  172,  173.  Eeductio  ad  absurdum, 
174. 


CHAPTER  V. 

THE  EMPLOYMENT  OF  GUESSWORK. 
SECTION 

I.  General  and  Special  Sources  of  Fallacy  176 

Aristotle's  plan  of  division,  176.     Mill's  plan  similar,  177. 
The  same  plan  largely  adopted  in  common  use,  177. 


XU  CONTENTS. 

SECTION  PAOB 

II.  A  List  of  General  Objections  to  any  Aegument  ...     178 

Four  main  general  objections,  178.  These  four  convenient 
but  overlapping,  178-181.  We  must  limit  their  meaning 
by  special  definition,  182. 

III.  The  Objection  Ignoratio  Elenchi        182 

Three  senses  of  the  term,  182.  Dangers  of  bringing  this 
accusation,  183-185.  Logic  and  Grammar,  183.  Use  of 
the  Law  of  Excluded  Middle,  185.  Snares  of  language 
inexhaustible,  186;  and  practically  inevitable,  187.  Ob- 
jections that  miss  the  point,  188.  Finer  shades  of  the 
fallacy,  188-191.  Change  in  the  meaning  of  words,  189. 
Meaning  relative  -to  a  standard,  191.  A  broad  rale  for 
practice,  192. 

IV.  The  Objection  Petitio  Principii  193 

Similar  difficulty  in  fixing  the  meaning,  193-195.  The 
meaning  here  taken,  195.  Means  of  escape  from  the 
accusation,  196,  197.  Resemblance  to  Platitude,  198. 
Question-begging  names,  198,  199. 


CHAPTER  VI. 

THE  EMPLOYMENT  OF  GUESSWORK:  CONTINUED. 

I.  The  Objection  'A  Factor  overlooked'       201 

Faults  of  the  name,  201.     Forms  of  this  fallacy  really  few 
and  simple,  202. 

II.  The  Tvpes  of  Argument  202 

§  1.  Introductory. 

§2.  Demonstration  and  Real  Proof      ...         ...         ...         ...     203 

Our  neglect  of  this  distinction,  203,  212.  Eeal  argu- 
ments and  Beal  propositions,  204.  Meaning  of 
*  Demonstration,'  204-207 ;  of  Conclusive  proof,  205 ; 
and  of  Necessary  truth,  207.  Immediate  and  Mediate 
demonstration,  208.  Causes  of  faulty  demonstration, 
209.  Demonstrative  arguments  rare,  209,  210. 
Omitted  links,  210,  211. 


CONTENTS.  Xin 

PAGE 

§  3.  Induction  and  Deduction 212 

Deductive  and  inductive  proof,  212-214,  219.  Theory 
and  fact,  213.  All  proof  deductive,  213.  DiflSculties 
of  the  distinction,  214-218.  Proof  of  theory  by 
congruent  fact,  219.    And  by  recognized  law,  219. 

§4   Certain  Minor  Distinctions  220 

Conclusive  and  presumptive  proof,  220.  Circumstantial 
evidence,  testimony,  hearsay,  221.  Hypothetical 
and  categorical  arguments,  221-223.  Moods  of  the 
Syllogism,  223.  Ad  personam,  ad  verecundiam,  ad 
populum,  223. 

§5.  The  Argument  hy  Example  224 

Difference  from  proof  by  circumstantial  evidence, 
224,  225.     Subdivision  to  be  made,  226. 

(a)  The  Argument  by  Analogy      226 

Indistinct  resemblance,  227.  Degrees  of  resem- 
blance, 227.  Points  of  resemblance,  228.  Essen- 
tial points  of  resemblance,  229,  230.  Formula  for 
analogical  argument,  230.  Difficulty  of  dis- 
tinguishing analogy  from  deduction,  231,  233. 
'Parallel  cases,'  233.  Connexion  between  ana- 
logical and  deductive  arguments,  234. 

(b)  Proof  of  Law  from  Fact  234 

A  generalisation  not  always  expressed  as  abstract, 

235.  Reasons  for  choosing  the  abstract  propo- 
sition  as  typical,  236.  The  '  essential  element ' 
of  the  cause,  237,  238.     Formula  for  the  indue 

1 6.  The  Argument  hy  Sign        ...         ...     239 

Middle  term  may  always  be  viewed  as  a  sign,  239 : 
but  need  not  always  be  so  viewed,  240.  Simplest  type 
of  deductive  argument,  240.  Second  type, — '  Distinc- 
tion by  point  of  difference,'  241.  Third  type, — '  Ex- 
ceptive disproof,'  241,  242.  Two  varieties  of  the  last, 
242.    Precaution  in  accepting  these  distinctions,  243. 

(a)  Proof  hy  Sign    ...         ...         ...         ...         ...         ...     244 

Generality  of  the  sign  required,  244,  245.  Nota 
NotoB,  245.     Names  as  labels,  245. 


xiv  CONTENTS. 

PAGE 

(b)  Distinction  hy  Point  of  Difference      ...         246 

Indistinct  difference,  246.  Essential  difference 
247,  248.  Negative  character  of  this  argument, 
248. 

(c)  Exceptive  Disproof       ...         ...         ...         ...         ...     249 

The  exception  proves  the  rale,  249,  250.  Difficulty 
of  proving  a  negative,  250,  251.  Value  of  ex- 
ceptions, 251,  252. 

SECTION 

III.  The  Dangers  of  the  Argument  by  Example    ...    ...  252 

(a)  The  Dangers  of  Analogy. 

Neglect  of  difference,  254^259.  Analogy  worthless  for 
proof,  256.  Analogy,  metaphor,  and  naming,  259. 
An  example  of  loose  analogy,  259,  260.  When 
allowable,  261.  Open  reliance  on  analogy  rare, 
262-264,  Metaphorical  and  direct  use  of  names, 
264-266.  The  employment  of  proverbs,  266.  The 
assertion  of  essential  resemblance,  266,  267.  The 
vital  point  of  an  analogy,  267. 

(b)  The  Dangers  of  Induction  ...         ...  ...         ...         ...     267 

Degrees  of  strength  in  '  indication,'  267-270.  '  Tenden- 
cies,' 268.  Sole  cause,  etc.,  269.  One  primary 
danger  in  induction,  270.  Undue  neglect  of  differ- 
ence, 270-273.  'Best'  explanation,  271,  272. 
Guarding  against  undiscovered  exceptions,  271.  Two 
opposite  modes  of  missing  the  ideal,  273.  Use  of  the 
Theory  of  Probabilities,  274.  Exclusion  of  alternative 
theories,  275,  276.     Need  of  analysis,  276. 

(c)  The  Empirical  Methods        ...         277 

The  use  of  the  methods,  277.  Number,  and  kind,  of 
'  congruent  facts,'  279.  Importance  of  analysis,  279. 
Attack  on  a  generalisation,  279-281.  Methods  of 
agreement  and  difference  fundamental,  281.  The 
distinction  between  them  unimportant  for  our  pur- 
pose, 282.  The  proof  of  laws  from  facts,  283,  284. 
Ubiquity  of  '  unknown  antecedents,'  284.  Results  of 
this  section,  285,  286; 


CONTENTS.  XV 

SECTION  PAGE 

IV.  The  Dangers  o?  the  Argument  by  Sign     ...        286 

Cawses  of  faulty  deduction  various,  287.  Acceptance  of 
a  Principle  which  does  not  apply,  288.  Ignorance  of 
syllogistic  requirements,  288.  Earity  of  purely  syllogistic 
fallacies,  289.  Acceptance  of  reciprocal  as  equivalent, 
290-292.  Fallacia  accidentis,  292-297.  Neglect  of  differ- 
ence, 295.    Neglect  of  resemblance,  296. 


CHAPTER  VII, 

REDUCTIO  AB  ABSURDUM 298 

Where  guesswork  fails,  what  then  ?  298.  Meanings  of 
fieduction  to  Absurdity,  299.  The  further  assertion  re- 
quired in  a  '  real '  argument,  299-301.  Gaps  in  the 
reasoning,  301.  Axiom  of  the  syllogism,  301,  302. 
Dictum  de  singulo,  301.  Uniformity  of  Nature,  302.  The 
case  where  the  application  is  direct,  303.  Extent  of  the 
Principle  involved,  304-307.  Interrogative  form  of 
the  method,  307.  The  case  where  the  Application  is 
remote,  308.  The  method  in  Analogy  and  Induction, 
309,  310.  Examination  of  rival  theories,  310,  311.  The 
negative  attitude,  311-313. 


CHAPTER  VIII. 

SOME  OBJECTIONS  TO  LOGIC  ...  ...  ...      314 

Practical  objections  broadly  divisible  into  two  groups,  314. 
Hindrance  to  action,  314-320.  Fallibility  of  Science,  318. 
Value  of  Error,  317-320.  Clumsiness  of  Logic,  320-3?  k 
Common-sense,  and  intuition,  321.  Need  for  deliberata 
reason  and  an  objective  standard,  322-324. 


CONCLUSION. 
Summary 825 


XVI  CONTENTS. 


APPENDIX. 

PAGE 

A.  Alternative  Possibilities  ,.        ...    333 

Erents,  to  be  named,  are  abstracted,  333.  The  Tarlous 
ways  in  which  any  two  events  may  be  related  to  each 
other  in  Causation,  334-338.  Co-existent  events,  335-338. 
Co-existent  qualities,  338.  Use  of  the  empirical  methods, 
339. 

B.  The  Empisical  Methods  in  Detail       839 

Mill's  five  methods  really  two,  339.  The  two  Axioms,  340, 
341.  Method  of  Agreement,  342.  Joint  Method,  344. 
Method  of  Difference,  345.  Method  of  Residues,  347. 
Method  of  Concomitant  Variations,  348.  The  Methods, 
in  general,  351.  The  further  evidence  required,  in  em- 
ploying each  method,  351,  352.  Simplex  enumeratio,  and 
Post  hoc,  352. 

C.  The  Moods  op  Exceptive  Disproof      353 

Reductio  per  impossibile,  353.  The  fourteen  moods  reduced 
to  two,  354r-356. 

D.  Invariable  Succession      356 

Cause  and 'history,' 356.  'Invariable  law'  and  'identity* 
of  cause  and  effect,  357.  Unconditionality  (Efficacy), 
858. 

E.  Tables. 

I.  Abstract  and  Concrete  FropositlooB. 
II.  Succession  and  Co-existence. 

III.  The  Questions  arising  from  Proof. 

IV.  The  Types  of  Argument. 

V.  The  Dangers  peculiar  to  the  special  types  of  Argament. 


FALLACIES. 


INTRODUCTION. 

I.  Difficulties  of  Treatment. 

Logic  holds  what  may  well  be  called  an  uncomfort- 
able position  among  the  sciences.  According  to  some 
authorities  it  cannot  be  properly  said  that  a  body  of 
accepted  logical  doctrines  exists:  according  to  others, 
the  facts  and  laws  that  form  such  doctrine  are  so  com- 
pletely undeniable  that  to  state  them  is  hardly  to 
convey  new  or  important  information.  Hence,  if  a  writer 
on  the  science  tries  to  avoid  truism,  and  so  to  give 
practical  importance  to  his  statements,  there  is  danger 
both  of  real  but  crude  innovation,  and  also  of  over-simple 
belief  in  the  value  of  merely  verbal  alterations.  More- 
over, at  its  best,  Logic  has  many  persistent  enemies,  and 
by  no  means  all  of  them  are  in  the  wrong :  so  that  those 
who  view  the  science  as  the  thief  or  burglar  views  the 
law,  find  themselves  apparently  supported  and  kept  in 
countenance  by  others  who  really  have  the  right  to  view 


2  FALLACIES.  [Introd. 

it  as  perhaps  the  artist  views  the  rules  that  hampei 
genius.  Through  its  deep  connexion  with  Common 
Sense,  Logic  is  often  a  source  of  exasperation  to  Philo- 
sophy proper :  while  Common  Sense  on  the  other  hand 
is  apt  to  dread  or  dislike  it  as  unpractical  or  over-fond 
of  casuistical  refinements.  Failing  thus  to  win  a  steady 
footing,  it  turns,  sometimes,  to  Physical  Science  for  a 
field  of  operations :  but  Physical  Science  has  its  proper 
share  of  boldness,  and  often  leaves  the  cautious  reasoner 
behind.  As  for  Art, — which  finds  even  Common  Sense 
too  rigid, — here  Logic  is  liable  to  meet  with  opposition 
at  every  grade ;  from  the  righteous  impatience  of  poetic 
souls  that  are  genuinely  under  grace,  down  to  the  in- 
coherent anger  of  mere  boastful  vagueness,  or  to  the 
outcry  of  the  sentimental  idler. 

In  the  midst  of  these  perplexities,  it  is  difiicult  to 
choose  a  quite  satisfactory  course.  Some  excuses  may, 
however,  be  offered  for  the  line  that  has  here  been 
taken;  and,  first,  I  would  plead  as  against  the  charge  of 
irregularity  or  presumption  the  fact  that  I  have  wished 
to  keep  a  single  purpose  in  view,  avoiding  all  questions 
that  fail  to  bear  directly  upon  it.  Usually,  in  works  on 
Logic,  the  object  has  been  to  say  something  valuable 
upon  all  the  questions  traditionally  treated  as  within  the 
field  of  the  science,  and,  in  attempting  this,  the  single 
practical  purpose  is  apt  to  become  obscured.  It  is  only 
in  consequence  of  my  avoidance  of  side-issues  that  any 
appearance  of  novelty  in  the  treatment  has  followed. 
Moreover,  it  is  not  teaching,  but  suggestion  that  is  chiefly 


Intkod.]  difficulties  OF  TREATMENT.  S 

here  intended.  It  is  always  allowable  to  write  rather 
in  the  co-operative  spirit  than  the  didactic,  and  this 
has  certainly  been  my  aim  throughout.  And  the  same 
apology  may  apply  to  the  charge  of  forcing  verbal 
changes  upon  the  reader :  the  novelties  of  statement  are 
here  put  forward  merely  as  possible  aids  in  keeping 
our  single  purpose  clear,  and,  in  fact,  I  found  them  almost 
unavoidable. 

As  regards  the  points  where  Logic  might  seem  to 
clash  with  the  furthest  or  deepest  Philosophy  attainable, 
the  plan  adopted  has  been  to  avoid  all  controversy  by 
restricting  our  discussion  to  the  questions  that  arise 
before  such  deepest  Philosophy  begins.  Without  ad- 
vancing any  opinion  on  the  merits  of  metaphysical 
inquiry  in  general,  or  on  any  of  its  particular  results,  I 
wish  to  confine  attention  to  a  totally  different  set  of 
problems. 

As  regards  Physical  Science,  it  must  be  confessed 
that  Logic  merely  follows  after  it,  systematising  methods 
already  adopted  there,  and  found  to  lead  to  good  results. 
And  I  hold  that  to  combat  Fallacy  is  the  7uison  d'etre 
of  Logic  ;  and  that  Science,  though  not  infallible,  is  more 
free  from  discoverable  fallacies  than  any  other  field  of 
thought.  Again,  while  experimental  methods  may  no 
doubt  be  capable  of  much  improvement,  it  seems  a 
tenable  view  that  this  duty  should  be  left  to  a  special, 
and  very  advanced,  department  of  inquiry.  There  might, 
perhaps,  be  formulated  a  system  of  advice  for  Discovery 
in  general,  —  rules  and  hints  important  even  to    the 


4  FALLACIES.  [Intbod. 

leading  men  of  science.  But  in  the  meantime,  Logic  (as 
usually  understood)  can  hardly  help  containing  a  good 
deal  of  elementary  matter,  and  is  compelled  to  take  for 
granted  in  the  learner  a  power  of  making  very  elementary 
mistakes.  It  seems  that  the  best  Scientific  Discovery 
must  always  be  in  advance  of  Inductive  Logic,  in  much 
the  same  way  as  the  best  employment  of  language  runs 
in  advance  of  Grammar.  Still,  there  may  be  some  use  in 
trying  to  direct  and  help  those  who  are  not  already 
scientific,  or  only  in  the  earlier  stages  of  the  pursuit ;  nor 
need  the  name  of  Logic  compel  logicians  to  claim  a 
dignity  beyond  their  power.  One  cannot  fulfil  success- 
fully the  duties  of  Lord  Chancellor  and  Justice  of  the 
Peace  at  once. 

As  regards  Common  Sense,  it  is  a  little  more  difiicult 
to  avoid  coming  into  conflict  here ;  since  there  are  plainly 
two  kinds  of  Common  Sense, — one  the  essence,  and  the 
other  an  undying  enemy,  of  the  most  perfect  use  of 
reason.  Against  near-sighted  dogmatism,  or  the  self- 
satisfied  refusal  to  see  distinctions,  or  the  habit  of  slurring 
over  awkward  facts.  Logic  always  intends  to  carry  on  a 
war :  but  we  need  not  therefore  assume  that  depth  or 
distance  of  vision,  or  the  practice  of  splitting  hairs  or  of 
raising  ingenious  doubts  and  difficulties,  can  never  be 
pushed  beyond  the  limit  at  which  they  possess  a  practical 
value.  The  drawing  of  this  line  is  a  standing  difficulty 
which  cannot  be  settled  off-hand,  but  needs  the  utmost 
patience  :  at  present,  it  seems  to  me,  one  can  only  admit 
the  difficulty  and  remember  that  the  needs  of  practice 


Intbod.]  difficulties  OF  TREATMENT.  5 

have  an  older  and  more  final  claim  than  those  of 
curiosity.  And,  mutatis  mutandis,  the  same  applies  to 
the  objections  from  the  side  of  Art:  here,  also,  two 
different  spirits  may  be  clearly  distinguished,  one  fighting 
really  on  our  side,  though  perhaps  by  other  methods, 
and  the  other  fighting  against  us  indeed,  but  an  enemy 
deserving  little  else  than  contempt  from  healthy  people. 

But  perhaps  the  special  difficulty  in  the  case  of 
Common  Sense  is  that  to  the  simple-minded  all  things 
are  simple  and  straightforward.  The  knowledge  of 
difiiculties  and  of  dangers  is  already  an  advance  beyond 
mere  childish  innocence  of  evil.  As  Mrs.  Farebrother,  in 
Middlemarch,  is  made  to  say,  "  When  I  was  young,  Mr. 
Lydgate,  there  was  never  any  question  about  right  and 
wrong.  We  knew  our  catechism  and  that  was  enough ; 
we  learnt  our  creed  and  our  duty.  Every  respectable 
Church  person  had  the  same  opinions.  But  now  " — alas ! 
the  reverence  for  easy-going  certainty  is  lost.  So  in  the 
kindred  question  of  bodily  disease :  to  our  grandfathers, 
and  still  more  to  their  grandfathers,  diseases  were  few  in 
number  but  quite  unmistakeable  when  they  came :  pre- 
monitory symptoms  were  almost  things  unknown,  and 
degrees  of  health  were  only  reluctantly  admitted  possible. 
And  yet  the  death-rate  is  decreasing :  our  ancestors  died 
by  thousands  of  diseases  which  we  are  conquering.  Very 
similar  is  still  to  a  great  extent  the  attitude  of  Common 
Sense  towards  Fallacy.  "  Did  God  make  men  two-legged 
only,  and  leave  it  to  Aristotle  to  make  them  rational  ? " 
Nothing  is  hg,rder  than  to  induce  short-sight  or  super- 


6  FALLACIES.  [Intbod. 

ficiality  to  believe  that  any  extension  of  view  or  of 
insight  exists  beyond  that  to  which  Common  Sense  is 
accustomed:  although  the  actual  telescope  and  the 
microscope  cannot  now  be  treated  as  mere  toys,  yet  out- 
side the  realm  of  material  objects  the  telescopic  and  the 
microscopic  spirit  is  still,  by  many,  considered  almost 
worse  than  useless.  The  general  reader  has,  in  fact,  a 
rooted  belief  that  Logic  is  a  highly  unpractical  body  of 
doctrine :  unpractical  perhaps  not  only  through  short- 
comings of  its  own,  but  from  the  supposed  fact  that  no 
one  but  an  absolute  fool  can  ever  commit  a  fallacy.  Is 
not  the  light  of  Nature  worth  more  than  all  the  reason- 
ings of  all  the  logicians  that  ever  lived  ?  Such  an  appeal 
to  idleness  is  always  sure  to  win  a  large  amount  of  ready 
applause.  The  view  here  taken,  on  the  contrary,  is  that 
many  things  are  believed  in  the  name  of  Common  Sense 
which  a  higher  Common  Sense  would  condemn,  and  that 
no  one  who  is  merely  human  can  avoid  fallacy  altogether 
for  a  day. 

Another  fact  moreover  which  operates  to  prevent  any 
widespread  interest  in  Logic  is,  no  doubt,  its  barrenness 
in  surprises.  In  all  the  physical  sciences.  Common  Sense 
is  being  constantly  forced  to  acknowledge  that  its 
methods  are  not  so  infallible  as  our  fathers  fondly 
supposed.  Even  the  question  "  Am  I  not  to  believe  my 
own  eyes  ? "  carries  no  longer  the  same  conclusiveness  as 
formerly,  while  every  day  some  new  portion  of  firmly 
held  popular  faith  is  shown  to  have  been  delusive  or  inT 
complete.     Nor  is  it  only  in  what  are  commonly  called 


Introd.]  difficulties   OF  TREATMENT.  7 

the  Physical  Sciences  that  this  is  the  case.  Political 
Economy,  though  it  depends  so  largely  on  mere  careful- 
ness and  consistency  of  thought,  is  rich  in  unsuspected 
facts.  In  Mental  Science,  and  perhaps  in  Ethics,  a 
harvest  of  surprises  is  ripening.  But  in  Logic  the  case  is 
different.  The  central  practical  doctrines  of  Logic  have 
been  so  long  ago  made  common  property  that  to  a  great 
extent  they  have  passed  into  commonplace:  which  is 
much  the  same  as  saying  that  they  commonly  command 
verbal  assent  too  readily  for  real  assent  to  be  strong. 
They  lose  the  strong  support  that  comes  from  conquered 
doubt,  and  through  supposed  familiarity  pass  into  real 
oblivion.  Hence  it  is  chiefly  in  generalising  what  is 
already  known,  and  so  preserving  it  in  a  shape  more 
easy  to  remember  and  apply,  that  the  value  of  Logic 
consists.  And  therefore  it  is  difficult  to  prevent  its 
doctrines  being  tedious  or  exasperating,  even  where  they 
may  be  most  required. 

There  are  one  or  two  minor  objections  to  the  study 
of  Logic, — even  practical  Logic — which  may  be  just 
mentioned  here  as  possible  stumbling-blocks.  One  some- 
times hears,  for  instance,  that  there  are  so  many  systems 
of  Logic  all  at  variance  with  each  other  that  the  puzzled 
inquirer  cannot  tell  which  to  accept.  On  this  it  seems 
sufficient  in  the  first  place  to  remark  that  Logic  does  not 
claim  to  be  a  sort  of  revelation,  which  any  one  is  requested 
to  'accept'  at  all,  but  rather  a  labour-saving  apparatus 
which  each  may  usefully  alter  somewhat  to  suit  his  own 
particular  needs.    Again,  it  is  hardly  too  much  to  say  that 


8  FALLACIES.  [Intbod 

whether  the  inquirer  thinks  for  himself,  or  accepts  the 
system  of  any  one  logician  or  of  all,  the  result  for  practical 
purposes  will  be  precisely  the  same,  except  perhaps  as  to 
speed  in  learning.  In  all  that  is  essential  to  practice 
there  is  not  only  no  difference  of  opinion  but  room  for 
none.  The  disputed  ground  of  Logic  lies  wholly  outside 
that  science  when  viewed  as  a  machine  for  combating 
Fallacy.  The  disputed  points  refer,  without  exception, 
either  to  the  question  of  the  proper  province  of  the 
science,  or  its  convenient  arrangement,  or  to  the  adja- 
cent subjects  of  Metaphysics,  Psychology,  Rhetoric,  or 
Grammar. 

Another  objection,  only  to  be  mentioned  as  unim- 
portant, is  that  the  study  of  Fallacies  belongs  altogether 
to  Rhetoric  rather  than  to  Logic,  and  to  Rhetoric  in  a 
degraded  form  The  effect  of  a  study  of  Fallacy,  it  seems 
to  be  sometimes  feared,  must  be  to  make  us  tricky,  or  at 
least  to  lead  to  wordiness  and  mere  ingenuity  of  repartee. 
But  let  us  at  any  rate  meet  part  of  this  objection  by  our- 
selves refusing  to  let  a  harmless  word  offend.  If  the  name 
Rhetoric  be  preferred  let  us  accept  that  name  without 
hesitation.  And  as  to  the  question  of  fact,  of  the  actual 
effect  of  a  study  of  Fallacies,  that  of  course  is  a  matter 
on  which  there  is  ample  room  for  difference  of  opinion, 
and  I  firmly  believe  that  such  study  has  on  the  whole  a 
depressing  and  disarming  effect  on  the  power  of  being 
successfully  sophistic,  even  where  the  will  to  deceive  is 
present.  For  really  effective  sophistry  nothing  is  so 
vitaUy  requisite  as  semi-innocence.     Just  so  far  as  the 


Inteod]  difficulties  OF  TREATMENT.  9 

epigram  holds  true  that  unconscious  hypocrites  are  the 
greatest  hypocrites  of  all,  so  may  we  say  that  the  self- 
deceiver  is  the  most  successful  sophist  Of  course,  by 
definition,  Fallacy  and  Sophism  are  distinct, — the  latter 
is  clever  deception,  the  former  only  honest  error ;  but  the 
line  between  them  is  in  real  life  so  dim  and  wavering 
that  the  distinction  is  practically  useless  for  most 
purposes  except  that  of  giving  our  neighbour  an  un- 
complimentary name.  Witness  the  case  of  the  highly 
respectable,  and  even  honourable,  man  who  late  in  life 
begins  to  find  cherished  theories  unstable.  By  the 
hypothesis  his  defence  of  them  can  be  considered  pure 
fallacy  no  longer,  and  yet  would  it  not  be  cruelly  unfair 
to  class  him  with  conscious  sophists  ?  Effective  sophistry 
of  the  more  conscious  kind  can  only  take  place  either 
where  the  audience  are  immensely  beneath  the  sophist 
in  acuteness  or  where  they  are  positively  eager  to  be 
deceived.  And  these  may,  from  a  general  point  of  view, 
be  regarded  as  exceptional  cases.  We  are  mostly  subject 
to  the  criticism  of  our  equals,  and  the  real  belief  is  widely 
held  that,  after  all,  truth  so  far  as  attainable  is  an  end  to 
be  desired. 

Another  objection  sometimes  heard  is  that  there  is 
danger  in  tampering  with  mother-wit  by  substituting  for 
it  the  highly  abstract,  narrow,  inelastic  rules  of  Logic. 
Real  life,  it  is  said,  is  large  and  complex  and  many- 
sided.  To  deal  with  actual  problems  successfully,  a 
quickness  and  breadth  of  perception  are  needed,  which 
must  be  largely  unconscious,  under  pain  of  being  in- 


10  FALLACIES.  [Iktbod. 

complete.  Much  in  the  same  way  as  the  hard  rules  of 
grammar  are  vexatious  to  those  who  know  their  mother- 
tongue,  or  as  a  deliberate  eflfort  to  remember  how  to 
spell  a  word  is  apt  to  raise  needless  doubts  and  difficul- 
ties, so,  it  is  sometimes  held,  does  highly  conscious 
reasoning  produce  more  evil  than  it  conquers.  This 
objection  has  some  real  force,  and  in  our  last  chapter 
there  will  be  occasion  to  speak  of  it  again.  At  the 
present  stage  it  may  be  sufficient  to  remark  that  although, 
no  doubt,  a  little  knowledge  is  a  dangerous  thing,  yet 
rightly  understood  that  fact  is,  in  ordinary  circum- 
stances, merely  an  argument  for  trying  to  attain  as 
much  knowledge  as  possible.  The  fact  of  the  danger 
once  recognised  too,  it  becomes  to  a  great  extent  disarmed. 
The  amount  of  knowledge  required  to  get  beyond  the 
dangerous  stage  in  Logic  is  easily  attained :  and  with  or 
without  that  knowledge  the  application  of  Logic  is  mainly 
dependent  on  practice  rather  than  on  theory.  All  that 
theory  can  expect  to  do  in  the  matter  is  to  clear  the 
way,  and  so  to  economise  a  great  deal  of  time  at  the 
beginning.  No  book  on  Logic  can  be  used  as  a  vade- 
mecum, — carried  in  the  pocket  and  consulted  when  in 
doubt  whether  to  take  a  cab  or  not,  and  in  other  daily 
difficulties  of  the  kind.  If  any  reader  is  inclined  to 
expect  such  aid  he  will  certainly  be  disappointed.  The 
point  of  view  and  the  expectations  must  be  altered, 
or  there  will  be  little  good  to  be  got  from  any  book. 
Nothing  can  be  a  complete  guarantee  against  all  fallacy; 
nor  can  Logic  be  made  an  instrument  for  testing  or 


Iotuod.]  the  practical  side  of  logic.  11 

judging  ofF-hand  the  truth  of  all  possible  propositions 
put  forward. 


II.  The  Practical  Side  of  Logic. 

We  are,  then,  not  here  properly  or  directly  concerned 
with  any  of  the  disputed  questions  of  Logic :  we  need 
not  even  discuss  the  nature  of  that  science  or  the  limits 
of  its  province.  And  yet  the  matters  we  shall  have  to 
treat  constitute  in  themselves  the  main  thread  which 
runs  through  all  logical  doctrine,  and  the  final  object  for 
which  it  has  been  developed.  By  making  the  practical 
purpose  of  Logic  the  central  point  of  interest,  we  help  to 
gather  up  and  bind  together  its  disconnected  parts 

Logic  may  in  fact  be  viewed  as  a  machine  for 
combating  Fallacy.  Like  all  machines,  too,  it  is  itself 
capable  of  much  improvement  in  the  certainty,  the  pace, 
and  the  fineness  with  which  it  performs  its  work.  But 
unlike  machines  of  lifeless  material,  its  final  purpose  is 
in  constant  danger  of  being  forgotten  for  other  interests, 
as  men  sometimes  lose  sight  of  their  main  intention,  take 
means  for  ends,  and  become  misers  or  enthusiasts.  Logic 
is  rather  a  living  organism  than  purely  mechanical,  and 
it  is  full  of  rudimentary  organs  which  have  historical 
and  explanatory  interest,  but  not  all  of  which  are  now 
any  longer  useful  for  performing  work  or  preserving  the 
life  of  the  science.  The  Logic  required  for  examinations 
is  thickly  over-grown  with  disputed  questions  properly 
belonging  to  other  departments  of  inquiry :  and  though 


12  FALLACIES.  [Inthod. 

many  of  these  discussions  are  of  great  value  in  them- 
selves, and  some  perhaps  also  for  developing  still  further 
the  theory  of  Logic ;  though  no  one  can  consider  himself 
a  thorough  student  of  the  science  until  he  knows,  at  least 
in  broad  outline,  the  history  of  these  disputed  questions, 
yet  there  are  points  of  view  from  which  we  may  use- 
fully neglect  them,  may  avoid  all  doubtful  matters,  fix 
attention  solely  on  the  practical  means  of  fighting  fallacy, 
and,  as  preliminary,  sum  up  the  admitted  doctrines 
which  bear  directly  on  that  purpose,  to  the  exclusion  of 
all  the  rest.  We  shall  neglect,  therefore,  all  inquiry  into 
the  proper  '  province '  of  Logic.  If  any  reader  prefers 
any  other  name  for  the  doctrines  here  treated,  no  objec- 
tion will  be  raised.  It  is  our  business  to  inquire  what 
the  doctrines  bearing  on  the  above-mentioned  purpose 
are,  not  what  they  may  best  be  called.  If  through  the 
employment  of  a  wrong  name  any  discoverable  error 
should  arise  at  any  point,  that  point  will  present  a  con- 
venient opportunity  for  correcting  our  definition.  Pro- 
visionally, however,  and  with  this  apology,  we  may  use 
the  name  of  Logic. 

Next,  we  shall  neglect,  as  said  above,  aU  *  ultimate  ' 
questions ;  all  questions  of  purely  metaphysical  interest. 
And  here  it  seems  necessary  to  remove  a  possible  miscon- 
ception. There  is  an  active  hostility  to  Metaphysics 
which  has  exasperated  some  metaphysicians  into  declaring 
that  we  cannot  do  without  them.  Metaphysics  of  some 
sort,  they  tell  us,  there  must  be.  The  only  alternative 
is  between  good  metaphysics  and  the  cheap  substitute 


iNxnoD.]  THE  PRACTICAL  SIDE  OF  LOGIC.  13 

that  Positivism  provides.  Without  stopping  to  inquire 
whether  possibly  other  alternatives  might  be  discovered, 
I  may  remark  that  what  is  here  meant  by  neglecting 
metaphysical  discussions  is  simply  leaving  the  decision 
of  the  question  which  system  of  metaphysics  is,  on  the 
whole,  the  best,  until  some  occasion  when  the  pressure 
of  more  immediate  practical  needs  has  been  relieved,  t 
The  most  ardent  metaphysician  would  hardly  contend 
that  an  unexceptionable  system  of  metaphysics  is  a 
necessary  of  daily  life ;  and  it  is  entirely  with  explana- 
tion and  prediction  regarded  from  an  everyday  point  of 
view  that  we  are  here  concerned.  Having  satisfied  more 
immediate  needs,  readers  can  proceed  for  themselves 
afterwards  to  the  more  remote.  The  attempt  to  begin 
with  Metaphysics,  however  natural  it  may  be,  is  rather 
too  much  like  attempting  to  write  a  flowing  hand  while 
we  ought  to  be  practising  pothooks.  It  is  a  fair  descrip- 
tion of  the  '  practical '  spirit  in  Logic,  to  say  that  it 
consists  chiefly  in  the  intentional  neglect  of  these  deepest 
difficulties. 

We  start  at  any  rate  with  all  assumptions  on  which 
the  meaning  and  use  of  language  depends;  and  with 
those  which  are  necessary  in  order  that  explanation  and 
prediction  (for  practical  purposes)  should  be  possible. 
We  assume,  for  instance,  that  the  distinction  between 
the  subjective  and  objective  Universe  has  a  real  value ; 
and  also  that  the  whole  Universe  may  be  usefully 
parcelled  off  into  definite  'nameable  things,' — objects, 
qualities,  events,  and  classes  of  these, — which,  for  all 


i%  FALLACIES.  [Intbod 

practical  purposes,  may  be  viewed  as  consistently  break- 
ing its  continuity.  As  corollaries  to  the  second  of 
these  assumptions,  or  as  an  amplification  of  it,  we  may 
accept  the  formulae  known  as  the  'Axioms  of  Con- 
sistency,'*— the  Laws  of  Identity,  Contradiction,  and 
Excluded  Middle.  Secondly,  as  regards  the  Metaphysics 
of  Causation,  we  avoid  the  ultimate  difficulties  simply 
by  stopping  short  before  they  are  reached,  and  by  con- 
fining our  attention  to  what  may  be  called  a  lower  point 
of  view.  We  assume  the  existence  of  uniformities  in 
Nature, — natural  laws  ;  the  narrowing  down  of  these 
into  exactitude  being  the  endless  problem  of  discovery, 
and  the  completest  knowledge  of  them  already  attained 
at  any  period  being,  for  that  period,  the  basis  of  all 
explanation,  prediction,  and  proof. 

The  difficulty  of  keeping  the  discussion  of  Fallacy 
clear  of  psychological  questions  will  be  obvious  to  all 
readers  of  Mr.  Sully's  recent  work  on  Illusions ;  but  the 
scientific  treatment  there  given,  a  treatment  of  the 
subject  directly  from  the  psychological  point  of  view, 
helps  to  absolve  us  here  from  attempting  to  deal  with 
its  difficulties.  Logic  is  always  in  some  danger  of  en- 
tanglement with  Psychology,  but  by  keeping  the  practical 
purpose  prominently  in  view,  we  probably  avoid,  better 
than  in  any  other  way,  confusion  between  the  two 
distinct  sets  of  questions.  It  is  only  with  the  regulative 
laws  of  thought  that  Logic  has  any  direct  concern.  What- 
ever psychological  doctrines  may  be  here  occasionally 
*  More  properly  '  Postulatea.'    Also  called  •  Maxima  : '  cf .  infra,  p.  105. 


IKTROD.]  THE  PRACTICAL  SIDE  OP  LOGIC.  15 

appealed  to,  must  accordingly  be  considered  as  of  quite 
secondary  importance. 

Aofainst  confusion  with  Rhetoric  we  shall  find  it  more 
difficult  to  guard.  The  connexion  between  Practical 
Logic  and  Rhetoric  is  extremely  close,  and  for  those 
whose  interest  lies  in  accurately  mapping  out  the 
boundaries  of  either  science,  must  no  doubt  be  very 
puzzling.  Rhetoric  is  commonly  considered  as  the 
science  of  Persuasion  (and  possibly  also  of  Pleasing)  by 
means  of  language, — persuasion  whether  to  true  or  to 
false  conclusions;  and  since  Persuasion  partly  depends 
on  showing  the  person  to  be  persuaded  an  appearance, 
whether  real  or  counterfeit,  of  truth  —  of  absence  of 
fallacy, — the  importance  to  it  of  a  thorough  familiarity 
with  Logic  is  obvious.  Rhetoric  can  hardly  exist,  in 
its  most  powerful  shape  at  least,  without  a  considerable 
knowledge  of  the  difference  between  sound  and  unsound 
reasoning.  It  may,  in  fact,  on  its  argumentative  side, 
be  viewed  as  an  embodiment  of  Practical  Logic,  used  by 
one  person  upon  another  or  others,  and  applied  in- 
differently either  in  aid  of  the  purposes  for  which  Logic 
properly  exists,  or  in  antagonism  to  them.  But  though 
Rhetoric  cannot  exist  without  Logic,  the  latter  science 
can,  it  seems  to  me,  exist  apart  from  the  former.  As  Mill 
expressed  it,  if  there  were  but  one  rational  being  in  the 
universe,  that  being  might  be  a  perfect  logician ;  Logic, 
in  this  sense,  is  in  fact  simpler  than  Rhetoric,  and 
preliminary  to  it. 

The  connexion  between  Logic  and  Grammar  is  per- 


16  FALLACIES.  [Intbod. 

haps  not  quite  so  confusing,  though  still  not  altogether 
easy  to  avoid.  Both  Logic  and  Grammar  sit  in  judgment 
on  the  meaning  of  assertions  made.  Both  are  con- 
cerned with  the  use  of  language,  and  both  lay  down 
rules  for  its  correct  employment.  In  one  sense,  there- 
fore, Logic  may  be  regarded  as  only  a  wider  Grammar ; 
not  indeed  as  presuming  to  dictate  the  absolute  meaning 
of  any  given  set  of  words,  but  as  legislating  unmistakably 
in  certain  cases  on  the  combined  meaning  of  any  two  or 
more  separable  assertions  when  their  separate  meaning 
is  already  agreed  upon  or  declared.  While  Grammar, 
for  instance,  tells  us  that  two  negatives  make  an  affirma- 
tive, Logic  takes  a  wider  view  and  says  in  effect  "  Use 
whatever  words  and  phrases  you  please  (however  ungram- 
matical)  so  long  only  as  their  meaning  is  clearly  agreed 
upon ;  but  having  agreed  on  the  meaning  of  vour  terms 
and  your  propositions,  two  contradictories  fill  a  Universe, 
and  to  deny  the  one  is  to  assert  the  other."  The  main 
difference,  perhaps,  is  that  while  Grammar  is  solely  con- 
cerned with  enforcing  the  prevailing  fashion  in  language, 
and  thus  with  preventing  solecism.  Logic  cares  not  at  all 
what  the  fashion  may  be,  insisting  solely  that  meaning 
shall  be  in  the  first  place  agreed  upon,  and  then  con- 
sistently preserved.  In  Logic,  a  largeness  of  interpre- 
tation is  needed,  which  is  quite  unknown  to  Grammar ; 
for  its  sole  concern  is,  through  preventing  inconsistency, 
to  strike  at  the  root  of  Fallacy.  At  the  same  time  it  is 
not  always  quite  easy  in  practice  to  keep  the  two 
purposes  wholly  distinct,  since  Logic  finds  great  con- 


IKTBOD.]  THE  PRACTICAL   SIDE  OF   LOGIC.  17 

venience  and  great  economy  of  time,  in  making  some  use 
of  accepted  Grammar,  A  certain  amount  of  Grammar, 
as  also  a  certain  amount  of  Psychology,  is  one  of  the 
necessary  foundations  for  any  effective  study  of  Logic. 
Accordingly,  while  we  shall  have  occasion  sometimes  to 
neglect  side-questions  interesting  in  themselves,  but 
whose  interest  is  of  grammatical  rather  than  logical 
importance,  yet  from  our  point  of  view  language  is  a 
necessary  instrument,  and  the  accepted  rules  of  its  em- 
ployment are  of  high  convenience ;  and  hence  it  may  no 
doubt  be  found  sometimes  a  little  difficult  to  separate 
the  two  interests  of  Logic  and  Grammar. 

In  short,  so  far  as  any  question,  whether  commonly 
treated  as  a  logical  one  or  not,  has  a  direct  and  obvious 
bearing  on  the  methods  of  combating  Fallacy,  to  that 
extent  it  will  deserve  our  consideration:  so  far  as  its 
bearing  on  our  main  purpose  either  cannot  be  traced, 
or  is  too  remote  and  lengthy  for  satisfactory  treatment, 
to  that  extent  we  shall  simplify  our  work  by  avoiding  it. 

The  practical  purpose  of  Logic  being,  then,  the 
guidance  of  our  reasoning  as  safely  as  possible  through 
the  dangers  to  which  it  is  exposed,  it  remains  to  explain 
and  to  limit  this  purpose  more  particularly.  '  Guidance ' 
is  slightly  ambiguous,  since  a  set  of  hints  and  rules  aimed 
purely  at  increasing  our  powers  of  discovery,  might  fairly 
be  held  by  some  to  come  under  this  designation.  But 
it  is  entirely  with  proof  that  we  shall  be  concerned: 
with  the  reflection  on  our  inferences,  not  with  inference 
or  discovery  itself  directly.      Indirectly,  of  course,  the 


18  FALLACIES.  [Iktbod. 

methods  of  proof  are  auxiliary  to  discovery,  but  it  is  of 
great  importance  to  keep  the  two  purposes  distinct.  For 
proof  there  must  always  be  in  the  first  place  a  proposition 
to  be  proved,  or  thesis;  while,  in  inference,  this  is  the 
final  goal  of  which  we  are  in  search,  and  which  is  then 
rightly  called  the  conclusion.  Roughly  speaking,  every 
thesis  is  of  course  itself  an  inference,  but  an  inference 
(or  conclusion)  does  not  becomes  a  thesis  for  proof  until 
we  reflect  upon  our  reasoning,  and  desire  to  examine  the 
strength  of  our  grounds  for  the  belief  Guidance,  there- 
fore, must  here  be  taken  to  mean  not  the  first  vague 
hints  that  may  set  us  on  the  track  of  a  fruitful  inference, 
but  the  methods  for  conducting  an  impartial  trial  upon 
conclusions  already  somehow  reached.  The  methods 
of  Logic  cannot  be  employed  for  the  direct  purpose 
of  enabling  us  to  reason,  but  only  for  that  of  enabling 
us  to  know  whether  in  a  given  case  we  have  reasoned 
correctly,  or  at  least  to  discern  where  the  weak  point 
in  our  certainty  must  lie. 

'Reasoning'  too  demands  explanation.  By  some 
(e.g.  Whately  and  Hamilton)  an  attempt  has  been  made 
to  restrict  the  name  to  the  process  of  unfolding  our 
conceptions,  syllogising,  or  concluding  from  generals  to 
particulars ;  errors  in  reasoning  being  taken  to  mean 
simply  failures  in  consistency.  In  this  sense  of  the 
term,  a  child  who  had  once  been  scalded  through  putting 
his  hand  into  a  basin  of  hot  water,  might  be  said  to 
reason  correctly  in  dreading  a  basin  of  cold  water  on 
the  next  occasion ;  but  he  would  then  "  reason  correctly  " 


Intbod]  the  practical   SIDE  OF  LOGIC.  19 

by  means  of  a  premiss  materially  false, — that  premiss 
being  of  course  some  such  universal  as  'All  water  in 
a  basin  will  scald,'  or  some  such  application  as  '  This 
is  hot  water.'  In  another  of  its  senses,  to  reason  is, 
as  Mill  puts  it,  simply  to  infer  (whether  provisionally 
or  reflectively)  any  assertion  from  assertions  already 
admitted.  And  since  Mill's  definition  is  perhaps  most  in 
accordance  with  ordinary  usage,  and  further  since  it 
enables  us  to  bring  under  consideration  the  dangers 
in  Inductive  or  Empirical  Proof,  it  is  in  this  sense  that 
we  shall  here  understand  the  term,  adding  however  that 
it  is  against  errors  in  reflective  reasoning  only  that  Logic 
can  at  all  undertake  to  guard. 

Methods  of  guidance  might  be  discussed  either  from 
the  positive  side  or  the  negative, — as  supplying  marks 
by  which  to  recognise  either  valid  evidence  or  invalid. 
The  latter  plan,  as  the  name  chosen  for  the  book  will 
have  already  shown,  is  adopted  here.  Not  only  is 
Fallacy  in  many  ways  more  interesting  than  correct 
reasoning,  but  this  view  of  the  subject  seems  to  me 
to  keep  before  us,  more  distinctly  than  could  otherwise 
be  done,  the  negative  character  of  practical  Logic.  The 
application  of  Logic  is  on  the  whole  rather  restrictive 
than  forward-moving.  As  already  said,  it  does  not 
discover,  but  it  proves,  or  tests,  discoveries  which  claim 
to  be  already  made.  Moreover,  in  proportion  as  this 
negative  or  questioning  spirit  becomes  habitual,  our 
chance  grows  stronger  of  avoiding  the  character  of  an 
advocate,  and  attaining  the  judicial  frame  of  mind.     The 


20  FALLACIES.  IIntrod. 

first  condition  of  all  for  avoiding  fallacy,  must  surely 
be,  as  Mr.  Spencer  expresses  it,  "  the  calmness  that  is 
ready  to  recognise  or  to  infer  one  truth  as  readily 
as  another."  But  besides  this  possible  disciplinary  ad- 
vantage, and  on  the  whole  more  important  than  it,  the 
fact  should  be  remembered  that  it  is  as  the  enemy  of 
Fallacy  that  Logic  must  always  find  its  application 
to  real  life :  Fallacy  occupies  much  the  same  position 
in  regard  to  the  science  of  Proof  that  disease  occupies 
in  regard  to  the  science  of  Medicine. 

In  speaking  of  the  negative  character  of  Logic  as 
a  practical  science,  we  must  not  however  imagine  that 
its  action  on  belief  is  purely  repressive.  Rather,  by 
repressing  the  natural  tendency  to  undue  belief,  we  earn 
the  right  to  be  doubly  secure  in  those  beliefs  that  stand 
the  trial  well.  Of  all  unpractical  habits  of  mind,  the 
purely  sceptical  habit,  so  far  as  it  can  exist,  is  perhaps 
the  least  satisfactory ;  and  if  Logic  really  led  no  further 
than  this,  there  would  be  strong  practical  reasons  for 
determining  to  blind  ourselves  to  its  truths.  But  perhaps 
it  may  be  found  possible  to  keep  the  dangers  of  Proof 
in  view,  while  still  remembering  the  central  purpose  for 
which  this  is  done ;  namely,  not  in  order  to  discard  as 
much  pretended  evidence  as  possible,  but  to  win  security 
in  our  beliefs,  through  taking  care. 

IIL  Outline  of  the  Work. 

The  war  against  Fallacy  is,  I  am  afraid,  far  jtoo 
large  an  enterprise  to  be  undertaken  by  any  one  book. 


Intbod.]  outline  of  the  work.  21 

or  indeed  by  any  one  author.  Whether  or  no  it  was 
possible  long  ago,  to  survey  the  whole  field  of  knowledge, 
both  in  general  and  in  detail,  laying  down  the  law  for 
all  men,  and  marking  out  the  line  between  truth  and 
falsehood  in  all  departments,  nothing  of  the  kind  is 
possible  now  :  no  one  at  the  present  time, — unless  abso- 
lutely unaware  of  the  modem  developments  of  Science, 
and  its  innumerable  fields  of  special  research, — will 
presume  to  oflfer  to  his  readers,  a  set  of  infallible  methods 
for  keeping  free  from  error.  There  would  be  great 
danger,  it  is  felt,  of  providing  something  not  much  more 
practical  than  Dr.  Watts'  rules  'for  the  right  use  of 
Reason/ 

But  there  are  certain  broad  laws  (which  may  with 
sufiicient  accuracy  be  called  Laws  of  Evidence  in  general) 
which  are  perfectly  universal  in  their  stringency,  and 
which  it  concerns  every  one  to  have  at  his  fingers'  ends. 
Properly  speaking  these  are  laws,  not  of  evidence  itself, 
but  preliminary  to  the  operation  to  which  the  name 
'judgment  of  evidence '  is  most  commonly  applied, — laws 
of  interpretation  (in  a  wide  sense  of  that  term),  or,  more 
exactly,  laws  of  the  implication  of  one  assertion  by 
another  or  others,  whether  the  process  of  the  given 
material  inference  be  from  the  general  to  the  particular, 
or  vice  versd.  The  law  here  called  that  of  'Counter- 
indication  '  *  may  be  mentioned  as  a  typical  example  of 
what  is  meant;  or  the  Maxims  of  Consistency,  above 
referred  to ;  or  again,  the  law  that  all  Proof,  to  be  really 

•  Cf.  infra,  p.  84 


22  FALLACIES.  [ISTfiOD. 

Proof,  requires  a  reference  to  some  wider  generality* 
than  the  thesis.  The  knowledge  of  such  laws  is  not  by 
itself  a  sufficient  safeguard  against  all  possibility  of  error, 
but  only  a  prior  condition  of  attaining  any  safety  in 
judging,  even  with  the  best  possible  special  knowledge, 
or  after  the  longest '  experience.'  Such  laws,  though  in 
reality  extremely  few  and  simple, — some  even  almost 
ludicrously  self-evident, — present  sufficient  difficulties,  in 
their  application,  to  render  the  study  of  them,  in  regard 
to  such  application,  a  subject  well  worth  careful  attention : 
and  a  part  of  this  task  is  what  lies  before  us  here. 

It  is  evident  that  several  different  purposes  in  study- 
ing Fallacies  may  be  distinguished.  There  is,  for 
instance,  the  purely  scientific  or  theoretical  interest, 
whether  as  regards  the  Psychology  of  error,  or  merely 
with  the  view  of  obtaining  an  exhaustive  list,  and 
a  clear  tabular  arrangement,  of  its  varieties.  Or  on  the 
other  hand  there  is  the  practical  interest  (which  may 
of  course  also  be  in  the  best  sense  scientific),  leading 
to  a  survey  of  the  methods  of  combating  Fallacy  in  the 
shapes  in  which  it  actually  occurs.  And  under  this 
second  head  certain  quite  distinct  purposes  must  further 
be  noticed  as  possible.  The  methods  of  combating  Fal- 
lacy admit  broadly  of  three  quite  separable  developments  : 
there  may  be  methods  for  (1)  simply  detecting  fallacies 
already  committed  by  ourselves  or  others ;  or  (2)  for  con- 
victing others  of  such  errors  when  found ;  or  (3)  methods 
aiming  at  the  attainment  of  the  completest  infallibility 

*  Cf.  infra,  pp.  112,  213,  329. 


Intbod.J  outline  OF  THE  WORK.  23 

possible.  Or,  as  we  might  more  briefly  express  the  same 
division,  methods  of  diagnosis,  cure  and  prevention. 

Of  these  various  subjects,  our  purpose  here  will  be  to 
neglect  (as  said  above)  the  Psychology  of  error,  and  to 
aim  at  obtaining  only  such  classification  of  the  various 
possible  forms  of  Fallacy  as  shall  be  of  use  for  one  oi 
more  of  the  three  practical  purposes  above  mentioned. 

Next  it  may  be  remarked  that,  of  these  three,  the 
last  would  be  a  truly  desirable  accomplishment,  but  that 
the  total  avoidance  of  Fallacy  being  a  comprehensive 
subject,  it  seems  better  to  attack  it  piecemeal,  and  by 
dejjrees.  The  second  demands  a  combination  of  logical 
and  rhetorical  considerations  for  which  neither  Logic  nor 
Rhetoric  can  be  said  to  be  as  yet  at  all  prepared :  this 
subject,  if.  less  comprehensive  than  the  last,  presents  at 
any  rate  a  dangerously  complex  problem.  Even  the  first 
question  (the  defection  of  Fallacy),  if  it  is  to  be  treated 
in  any  thorough  manner,  offers  practical  difficulties  which 
might  well  render  us  content  with  a  less  ambitious  aim  : 
but  since  this  first  question  is  really  preliminary  either 
to  success  in  controversy,  or  to  the  avoiding  of  Fallacy, 
the  most  effectual  course  appears  to  be  to  inquire  in  the 
first  instance  what  can  be  done  towards  the  accomplish- 
ment of  this  simpler  purpose.  The  power  of  detection  is 
in  fact  the  first  stage  towards  avoidance ;  which  follows 
gradually,  as  detection  becomes  habitual. 

We  shall  find,  however,  that  this  purpose  itself  admits 
of  being  divided  further.  Some  only  of  its  elements,  as 
preliminary  to  the  whole  problem  of  the  detection  of 


24  FALLACIES.  IIntbod. 

Fallacy,  will  constitute  the  matters  for  our  consideration. 
As  already  said,  we  shall  be  concerned  mainly  with  the 
methods  of  Proof  and  Disproof,  and  with  the  points  at 
which  any  case  of  attempted  Proof  or  Disproof  is  liable 
to  break  down.  In  this  way,  at  least,  a  rough  ground- 
work will  be  laid,  from  which  any  of  the  practical 
questions  may  afterwards  be  approached.  The  mere 
laying  of  such  foundations  should  of  itself  help  materially 
in  the  detection  and  avoidance  of  Fallacy, — though  it  can 
of  course  contribute  nothing  to  their  exposure  so  far  as 
this  lies  beyond  and  outside  detection. 

Shortly,  then,  the  work  before  us  is  to  survey, 
classify,  explain,  and  illustrate  the  possible  objections 
which  can  be  brought  against  any  belief,  so  soon  as  it  is 
definite  enough  to  take  shape  in  language,  and  thereby 
to  become  a  thesis  for  proof.  An  exhaustive  review  oi 
possible  objections  once  taken,  the  formation  of  methods 
for  detecting  and  avoiding  Fallacies  becomes  less  difficult ; 
and,  accordingly,  some  suggestions  are  incidentally  made 
for  carrying  on  the  work  towards  this  goaL 

Since  any  pretended  assertion  may  be : — 

1.  Meaningless: 

2.  Mere  unsupported  assertion : 

3.  Insecurely  supported : 

this  will  constitute  our  main  primary  division.  In  the 
first  case,  of  course,  cadit  qucestio  as  to  the  truth  of  the 
assertion.  In  the  second  case  we  have  to  reckon  with 
the  Burden  of  Proof.  And  finally,  if  a  reason  be  given 
for  belief,  our  judgment  of  its  force  must   depend  pri- 


Introd]  outline  of  THE  WOEK.  25 

niarily  on  the  extent  and  soundness  of  our  knowledge  of 
the  methods  of  proof;  afterwards,  en  our  knowledge  of 
the  special  subject  in  question. 

"  People  talk  about  evidence,"  it  has  been  said,  "  as 
if  it  could  really  be  weighed  in  scales  by  a  blind  justice. 
No  man  can  judge  what  is  good  evidence  on  any  par- 
ticular subject,  unless  he  knows  that  subject  well."  This 
is  perfectly  true :  knowledge  of  the  special  subject  is 
required  before  we  can  judge  of  the  material  truth  of  all 
that  our  reasons  formally  imply.  But  so  long  as  igno- 
rance of  these  formal  implications  themselves  exists,  the 
methods  of  Logic  have  useful  work  to  do.  It  is  just  in 
making  clear  what  these  formal  implications  are, — in 
making  us  aware  of  the  full  extent  of  our  assertion  when 
we  bring  forward  any  reason  in  support  of  any  thesis, — 
that  the  central  practical  interest  of  Logic  consists. 
Beyond  this,  in  fact,  it  cannot  go :  in  Logic  as  in  Law 
Ignorantia  facti  excusat,  ignorantia  juris  non  excusat 
It  may  be  added,  however,  that  there  is  no  immediate 
danger  of  Logic's  occupation  coming  to  an  end.  People 
still  commit  purely  logical  blunders,  quite  apart  from 
any  ignorance  of  the  special  subject. 

Next,  whatever  reason  is  given  in  support  of  an 
assertion  made  may  fail  to  prove  it  in  either  of  two 
ways.     It  may  be : — 

(1)  Materially  false,  even  if  sufficient : 

(2)  Formally  insufficient,  even  if  true  : 

With  the  truth  of  the  Reason  given  we  have  nothing  to 
do  in  Logic.    That  is  to  say,  we  can  only  call  for  its 


26  FALLACIES.  [Inteod. 

supports,  for  the  supports  of  these  again,  and  so  on  until 
we  reach  some  ground  sufficiently  firm.  Accordingly, 
a  knowledge  of  the  requirements  of  formal  adequacy 
(apart  from  the  question  of  material  truth)  is  not  only 
all  that  any  science  of  Reasoning  can  provide,  but  so  far 
as  complete,  would  be  a  safeguard  against  all  discoverable 
error.  The  point  at  which  logical  doctrine  jper  se  falls 
short  of  this  complete  success,  has  been  above  vaguely  in- 
dicated. Later  we  shall  be  in  a  better  position  for  seeing 
more  definitely  how  far  the  help  of  Logic  alone  can  carry  us. 
Finally,  the  reason  or  reasons  given  in  support  of  an 
assertion  either  include  in  themselves  the  Toeaning  of 
that  assertion  or  do  not.  In  the  former  case  the  question 
as  to  their  material  truth  becomes  at  once  all-important ; 
in  the  latter  case  the  central  operation  of  Logic  begins. 
For  if  the  Reason  given  does  not  already  include  the 
Thesis  in  its  meaning,  some  other  assertion  is  required  to 
complete  its  binding  force :  and  it  is  in  the  adding  of 
this  further  assertion  that  aU  the  danger  lurks.  The 
theory  of  Proof  in  general  will  guarantee  our  supplying 
the  further  assertion  correctly ;  while  it  is  the  question 
of  the  material  truth  of  such  further  assertion  that  often 
depends  in  great  measure  on  our  knowledge  of  the  special 
subject. 

Our  work,  therefore,  will  consist  first  of  all  in  a  pre- 
liminary survey  of  the  nature  of  Proof  in  general,  its 
subject-matter  and  its  process.  Having  cleared  the 
ground  in  this  manner,  we  shall  proceed  to  take  in  detail 
the  objections  which  can  possibly  be  brought  against 


Introd.]  outline   of  THE  WORK.  27 

any  assertion,  dealing  first  with  those  objections  which 
arise  before  Proof  begins,  and  afterwards  with  the  various 
points  at  which  any  case  of  attempted  Proof  is  liable  to 
frustration.  Under  this  last  head  will  be  found,  in  one 
sense,  the  main  difficulty;  since  here  we  shall  have  to 
consider  to  some  extent  the  different  dangers  introduced 
by  the  different  varieties  of  Proof  It  is  hoped,  however, 
that  these  minor  distinctions  will  not  unduly  obscure 
our  more  general  view.  In  all  cases  where  real  (as  op- 
posed to  verbal — Cf.  p.  204)  reasons  are  brought  forward 
in  support  of  an  assertion,  the  operation  of  Logic  consists 
in  forcing  into  explicitness  whatever  is  implied  beyond 
that  which  directly  appears.  The  central  point  of  in- 
terest throughout  is  the  accurate  determination  of  the 
further  assertion  implied  in  giving  any  Reason  in  support 
of  any  Thesis. 


p" 


PART   I. 
PBOOF   IN    GENEBAL. 


CHAPTER  T. 
THE  MEANING  AND  AIMS  OF   PROOF. 

I.  Proof  and  Inference. 

One  of  the  distinctions  which  it  is  most  difficult,  and  at 
the  same  time  most  important,  to  keep  in  view,  is  that 
between  Proof  and  Inference.  In  any  treatment  of 
Logic,  confusion  of  these  two  separate  processes  is  likely 
to  lead  to  much  obscurity;  and  for  us  such  confusion 
would  be  certainly  fatal,  since  our  main  object  is  to  sim- 
plify as  far  as  possible  the  highly  complex  problem  which 
the  avoidance  of  Fallacy  presents,  attacking  in  the  first 
place  the  most  preliminary  difficulties :  and,  as  will  pre- 
sently become  evident,  the  detection  of  Fallacy  is  closely 
bound  up  with  the  whole  question  of  the  needs  and 
dangers  of  Proof,  while  the  attainment  of  methods  for 
rendering  our  inferences  secure  corresponds  more  nearly 
to  the  wider  and  deeper  problem  of  avoiding  Fallacy 
altogether. 

Nor  will  it  be  sufficient  for  us  to  rest  content  with 
the  brief  and  easy-going  dismissal  of  the  difficulty  which 
is   sometimes   accepted.     It  may  be  perfectly  true,  as 


32  FALLACIES.  [Past  I. 

Whately  (e.g.)  says,  that  "Reasoning  comprehends  In- 
ferring and  Proving,  which  are  not  two  different  things, 
but  the  same  thing  regarded  in  two  different  points  of 
view :  like  the  road  from  London  to  York,  and  the  road 
from  York  to  London ;"  but  if  London  happens  to  be  the 
place  we  want  to  reach,  it  becomes  a  matter  of  some  im- 
portance to  distinguish  carefully  between  the  two  dif- 
ferent directions.  It  wiU  not  suit  us  to  find  ourselves 
eventually  either  in  York,  or  wandering  for  ever  between 
Grantham  and  Peterborough.  For  neither  of  these  results 
shall  we  derive  much  consolation  from  reflecting  that  it 
is  "  the  same  road,  only  regarded  from  two  different  points 
of  view." 

'Inference'  is,  in  fact,  a  highly  ambiguous  word, 
capable  of  being  applied  to  Proof  as  well  as  to  Discovery ; 
and  all  round  the  question  lie  a  number  of  further  verbal 
ambiguities.  When  we  infer  one  fact  from  another  or 
others,  we  believe  that  fact  '  by  reason  of  our  belief  in 
those  others ;  and  when  we  prove  one  fact  by  means  of 
another,  exactly  the  same  expression  is  commonly  used. 
In  both  cases  there  is  '  reasoning/  and  accordingly  both 
that  from  which  the  inference  is  drawn  and  that  on 
which  the  proof  is  based  are  indiscriminately  called,  in 
popular  language,  the  '  reason.'  We  reason  when  we 
proceed  from  premisses  to  conclusion,  arriving  at  new 
truths  by  means  of  old  ones ;  and  we  reason  when,  having 
already  a  thesis  (an  assertion)  before  us,  we  produce 
arguments  to  support  it,  even  if  such  arguments  be  then 
for  the  first  time  thought  of.    Again, '  premisses '  is  some- 


Chap.  I.]        THE  MEANING  AND  AIMS  OF  PROOF.  33 

times  used  for  the  grounds  of  Proof,  and  sometimes  for 
the  data  of  Inference :  '  conclusion '  sometimes  means 
that  which  is  discovered;  and  sometimes  that  which 
is  proT^ed.  These  ambiguities  are  probably  one  great 
source  of  confusion  in  the  matter ;  but  besides  the  merely 
verbal  connexion  between  Proof  and  Inference,  and  per- 
haps in  fact  a  cause  of  it,  there  is  also  a  deeper  and  real 
connexion  to  which  still  more  of  the  difficulty  may  be 
traced.  Before  we  can  infer  safely,  we  must  prove  ;  but 
before  we  can  prove,  there  must  be  some  belief  set  up  for 
proof,  and  belief  (at  least  in  its  more  definite  forms) 
always  draws  a  large  part  of  its  life  from  prior  beliefs, 
and  is  therefore  already  an  inference.  There  are,  in  fact, 
'  inferences '  and  *  inferences,' — our  first  vague  guesses, 
and  the  last  assured  results  of  careful  inquiry  and  copious 
hostile  criticism.  Again,  in  some  cases  and  to  some 
extent,  the  reasons  to  which  we  appeal  as  proof  of  a 
given  belief  are  exactly  those  which  in  fact  led  us  to 
the  belief  in  question.  This  is  indeed  far  from  being 
always  the  case,  since  in  very  many  instances  the  causes 
of  a  belief  are  too  numerous  or  too  shadowy  to  be  remem- 
bered in  detail,  or  even  to  be  summed  up  in  any  concise 
expression.  We  need  not  base  this  assertion  on  any 
reference  to  the  more  physiological  causesof  belief :  quite 
apart  from  the  uncertainty  of  these,  and  even  assuming 
the  causes  of  belief  to  be  purely  intellectual,  who  can 
tell  exactly  why  he  believes  his  neighbour  worthy  or 
unworthy  of  confidence  ?  Or  who  can  sum  up  satisfac- 
torily the  multitude  of  indefinite  observations  that  go  to 


34'  FALLACIES.  [Pabt  L 

support  the  judgment, '  That  is  a  well-dressed  woman,'  or 
'This  is  a  windy  sky :'  what  are  the  signs,  exactly,  by 
which  we  recognise  a  friend's  step,  or  feel  the  pulse  of  an 
audience,  or  judge  some  work  of  art  ?  In  these  and  many 
other  cases  only  a  small  part  of  the  real  cause  can  ever 
be  given  as  a  reason.  Nevertheless,  the  causes  of  our 
belief  may  often  be  appealed  to,  if  we  can  remember 
them,  as  a  reason  for  believing :  the  same  facts  may 
be  grounds  of  Inference  and  of  Proof. 

As  a  preliminary  step,  then,  we  may  find  some  advan- 
tage in  correcting  these  ambiguities  by  the  employment 
of  two  different  names.  Althouo^h  'Inference'  mifflit 
no  doubt  fairly  be  taken  as  having  both  a  forward 
and  a  backward  reference,  thus  covering  both  fields — 
Discovery  and  Proof, — there  will  be  great  convenience 
in  restricting  it  as  far  as  possible  to  the  former  of 
these  two  meanings ;  *  and  also  in  keeping  the  expres- 
sions '  a  conclusion ' '  drawn  from '  (or  'following  from')  its 
'premisses'  (or  'data')  tor  the  case  of  Inference,  and  using 
for  the  case  of  Proof  the  expressions  '  a  thesis '  '  guaranteed 
by '  its  '  reasons '  (or  '  resting  upon '  its  '  grounds ').  By 
the  name  Inference  we  denote  the  process  of  reaching 
a  belief:  by  Proof  we  mean  the  process  of  establishing 
it  on  a  firm  foundation  after  it  is  already  somehow 
reached.  The  inferred  belief,  before  reflection  on  its 
validity  begins,  is  not  yet  a  thesis  with  reasons  given : 

*  Chiefly  because  'Discovery' — the  only  other  name  which  seems 
at  all  applicable  — is  apt  to  fix  attention  rather  on  the  result  than  on  the 
process. 


Chap.  I.]        THE  MEANING  AND  AIMS  OF  PROOF.  85 

these  only  come  into  existence  when  we  begin  to  test 
the  foundations  of  a  belief  put  forward  as  secure. 

The  problem  of  Proof  is  thus  always  narrower  and 
more  definite  than  that  of  Inference.  Instead  of  asking 
at  large  '  What  conclusion  may  be  drawn  ?  *  Proof  asks 
*  Is  such  and  such  a  given  conclusion  warranted  ? '  In- 
stead of  *  What  is  the  cause,  or  efiect,  or  nature,  of  A  ? ' 
or  *  What  is  the  law  involved  ? '  Proof  asks  '  Does  X 
stand  to  A  in  this  relation  ? '  '  Is  such  and  such  a  law 
the  true  one  ? '  Instead  of  having,  for  answer,  to  choose 
amongst  all  the  letters  of  an  indefinitely  long  alphabet, 
Proof  has  only  to  decide  between  the  two  alternatives, — 
Yes,  or  No. 

II.  Proving  and  Testing. 

It  must  not,  however,  be  supposed  that  by  thus  con- 
trasting Proof  with  Inference  all  has  been  done  that  is 
necessary  to  bring  out  its  full  meaning  and  to  avoid 
all  ambiguity.  Is  Proof  the  finding  of  guarantees,  or 
their  examination  when  already  found  ?  Is  it  the 
attempt  to  establish  a  given  belief,  or  the  attempt  to 
break  it  down,  or  neither  of  these  exactly  ? 

In  this  matter  also  popular  usage  is  not  consistent, 
though  on  the  whole  it  leans  rather  to  the  meaning  that 
makes  Proof  consist  in  the  finding  of  guarantees.  If  the 
view  here  taken  be  correct,  there  is  a  possible  reconcilia- 
tion between  these  apparently  opposite  meanings,  and 
either  by  itself  is  merely  incomplete.  For  some  purposes, 
no  doubt,  it  may  be  sufficient  to  say  that  proving  a  belief 


36  FALLACIES.  [Pabt  I. 

consists  in  establishing  its  truth,  but  this  definition  after 
all  carries  us  only  a  very  short  way.  Nor  will  it  suffice, 
when  asked  further  how  a  truth  is  to  be  established,  to 
answer  that  the  process  consists  in  'stating  a  valid 
reason'  for  the  belief  in  question.  This,  too,  is  true  as 
far  as  it  goes :  to  prove  an  alibi,  for  instance,  or  to  prove 
the  defendant's  guilt,  means  to  establish  the  truth  of  the 
assertion  that  the  defendant  was  elsewhere,  or  is  guilty ; 
and  no  doubt  the  process  always  consists  in  showing  a 
valid  reason  why  the  assertion  should  deserve  belief.  So 
a,gain,  to  prove  that  the  angles  at  the  base  of  an  isosceles 
triangle  are  equal  to  one  another,  means  to  establish  the 
truth  of  that  proposition ;  and  the  manner  of  performing 
the  process  certainly  is  by  showing  a  valid  reason,  or  a 
set  of  valid  reasons,  why  we  should  believe  it  to  be  true. 
But  there  is  an  important  fact  about  the  meaning  of 
Proof  which  this  explanation  tends  to  make  us  overlook. 
The  word  Proof,  like  so  many  other  words,  has  under- 
gone a  change  of  meaning  in  the  course  of  its  history. 
In  old  times,  to  prove  anything  meant  simply  to  test  it, 
to  see  what  strain  it  would  bear  or  what  fault  could  be 
found  with  it.  Nothing  was  implied,  one  way  or  the 
other,  as  to  the  result  of  the  inquiry :  the  thing  to  be 
proved  might  pass  the  examination  with  honours,  or 
might  fail  ignominiously,  but  in  either  case  the  proof 
took  place.  Thus,  "  the  exception  proves  the  rule  "  meant 
simply  that  the  exception  tries,  or  strains,  the  rule :  "  I 
have  bought  five  yoke  of  oxen  and  must  needs  go  and 
prove  them "  referred  merely  to  the  need  of  trying  the 


OuAP.  I.]        THE  MEANING   AND  AIMS   OF   PROOF.  37 

oxen,  or  testing  their  working  power.  And  to  soine 
extent  this  old  meaning  may,  perhaps,  be  said  still  to 
remain  in  use;  to  take  a  thing  'on  probation'  still 
allows  us  to  contemplate  the  possibility  of  discarding  it 
later  as  useless,  to  'probe'  is  a  confessedly  tentative 
pursuit,  and  a  lover  may  '  prove  untrue.' 

It  is,  of  course,  often  misleading  to  attempt  to  find 
the  modern  meaning  of  a  word  by  tracing  its  history. 
In  very  many  cases  any  attempt  to  bind  words  down  to 
their  ancient  meaning  would  lead  to  serious  error.     And 
yet  if  the  historical  inquiry  be  properly  guarded,  it  may 
sometimes  serve  to  throw  a  light  on  the  modem  meaning 
which  would  otherwise  be  lost  or  overlooked.     We  must 
certainly  avoid   supposing  that  to   prove   an  assertion 
means  nowadays  simply  to  subject  it  to  tests,  but  at  the 
same  time  by  remembering  this  ancient  sense  we  learn 
some  facts  about  the  meaning  and  aims  of  Proof  which 
are  really  inseparable  from  it,  and  which  the  modern 
employment  of  the  word  rather  too  much  tends  to  hide. 
Be  this,  however,  as  it  may,  for  our  purposes  at  any  rate 
it  is  in  attack  rather  than  in  establishment  that  the 
interest  lies ;  or  at  least  only  in  such  establishment  as  may 
be  won  in  open  battle.     Our  concern  with  Proof  differs 
from  that  of  the  advocate  in  that  we  are  not  interested 
in  the  finding  of  evidence  to  support  a  thesis,  but  only 
with  the  judging  of  evidence  already  put  forward;  or, 
on  the  other  hand,  dismissal  of  the  case  when  all  evidence 
is  wanting  or  when  no  definite  issue  can  be  joined. 

Viewing  Proof  as  essentially  consisting  in  successful 


38  FALLACIEa  [Pabt  L 

resistance  to  attack,  we  in  the  first  place  keep  before  our 
minds  the  limit  of  dogmatism  beyond  which  no  real 
proof  can  carry  us.  It  is  true  that  assertions  which  have 
been  tested  so  far  as  our  tests  can  go,  stand  in  a  better 
position  as  regards  trustworthiness  than  assertions  which 
have  not  been  tested ;  and  since  in  multitudes  of  cases 
the  tests  applied  are  amply  sufiicient  for  all  practical 
purposes,  Proof  has  come  in  course  of  time  to  mean 
chiefly  establishment  on  a  sound  basis.  Even  the  com- 
pletest  establishment  of  a  truth  is,  no  doubt,  limited  by 
our  very  finite  power  of  applying  tests  to  it ;  but  this  we 
easily,  and  for  the  most  part  wisely,  forget  in  the  pre- 
sence of  the  plain  and  fruitful  fact  that  our  power  of 
testing  belief  is  in  so  many  cases  practically  suflBcient. 
It  would  be  pedantic  and  absurd  to  be  always  re- 
membering that  our  tests  may  after  all  be  incomplete. 
When  we,  or  those  whom  we  accept  as  sufficient 
authority,  have  tested  the  assertion  that  the  earth  is 
round,  or  that  matter  gravitates,  it  will  be  found  on  the 
whole  more  useful  to  act  on  all  occasions  precisely  as  if 
those  assertions  were  absolutely  true.  Having  arrived 
at  Melbourne  by  way  of  Suez,  we  should  hardly,  through 
modesty  as  to  the  limits  of  human  knowledge,  hesitate 
to  sail  for  Europe  again  in  an  easterly  direction.  The 
belief  that  the  earth  is  round  is  certainly  only  proved — 
only  tested  and  not  yet  found  wanting, — but  we  get  from 
our  tests,  in  that  case  and  in  many  others,  a  kind 
of  certainty  which  on  the  whole  it  is  wiser  not  to 
doubt.     Fallible  though  we  are,  and  incomplete  though 


Chap.  I.]        THE  MEANING  AND  AIMS  OF  PROOF.  39 

our  methods  of  proof  or  testing  may  be,  yet  there  are 
strong  practical  reasons  for  considering  our  knowledge 
in  some  cases  perfectly  secure,  certain  kinds  of  proof 
sufficiently  complete. 

Although,  then,  simply  testing  is  in  this  way  the 
root-idea,  or  original  intention,  of  the  word  Proof,  the  full 
meaning  we  shall  understand  by  it  is  establishment  by 
means  of  tests  ;  or,  more  fully,  establishment  in  the  face 
of  hostile  criticism.  Not  until  both  sides  of  a  case  are 
heard  can  the  verdict  claim  to  be  of  real  value;  and  if 
we  accept  a  conclusion  without  considering  how  far  the 
facts  will  support  an  opposite  one,  we  do  so  at  our  peril. 
Thus,  in  fixing  the  meaning*  of  a  name,  the  point  of 
practical  importance  is  where  to  draw  the  line,  or  how  to 
distinguish  the  thing  in  question  from  other  things ;  in 
establishing  an  explanation,  a  law  of  nature,  or  a  pre- 
diction not  yet  verifiable  by  the  event,  the  important 
point  is  to  exclude  all  alternative  theories.  We  know, 
for  instance,  what '  work '  is,  roughly,  and  we  use  words 
like  '  civilisation '  or  '  honourable  ' — and  even  terms 
aiming  at  greater  definiteness,  as  *  animal,'  '  vegetable,* 
'man,'  and  'beast' — with  the  utmost  glibness,  and  with 
a  fair  amount  of  sense  :  but  the  whole  difficulty  of  fixing 
their  definitions,  or  settling  their  exact  meaning,  begins 
when  we  attempt  to  draw  the  line  dividing  them  from 
their  opposites;  when,  in  fact,  we  try  to  justify  our 
exclusion  of  certain  candidates  for  the  title.  We  must 
know  clearly  what  is  not  work,  if  we  are  to  find  the 

♦  See  also  pp.  93,  106, 133,  inf. 


4©  FALLACIES.  [Pabt  I. 

stricter  applications  of  the  word ;  we  must  determiiicj  (if 
possible)  where  civilisation  ends  and  its  opposite  begins, 
or  what  are  the  exact  points  of  difference  which  separate 
animal  from  vegetable,  man  from  beast.  Again,  before  we 
can  consider  any  theory  proved,  whether  such  theory  be  a 
sweeping  law,  like  that  of  gravitation,  or  an  explanation 
or  prediction  of  some  one  actual  event,  we  must  have 
sound  reasons  for  excluding  every  possible  rival  theory. 

This,  at  least,  would  constitute  complete  Proof,  if  such 
could  ever  be  attained :  so  far  as  it  falls  short  of  this,  our 
proof  is  weak.  The  exhaustive  examination  of  alterna- 
tive theories  is  of  course  an  ideal  which  we  cannot  com- 
pletely reach;  but  the  nearer  we  approach  to  it,  the 
more  thorough  is  our  proof,  the  less  assailable  our  cer- 
tainty. Thus  assertions  stand  on  a  varying  scale  of 
credibility:  which  is  only  another  way  of  saying  that 
evidence  varies  in  strength. 

In  proportion  as  the  attacks  resisted  represent  all 
possible  attacks,  Proof  is  complete.  Hence  the  importance 
of  our  central  question, — On  what  grounds  can  any  asser- 
tion be  attacked  ?  And  first  we  need  a  general  view  of 
the  nature  and  varieties  of  assertion ;  a  classification  of 
the  questions  that  may  arise  for  Proof. 


CHAPTER  II. 

THE  SUBJECT-MATTER  OF  PROOF:   IN  GENERAL. 

I,   Real  and  Unreal  Propositions. 

Having  sketched  thus  in  outline  the  distinction 
between  Proof  and  Inference  (the  only  other  process  with 
which  Proof  is  liable  to  be  confounded),  the  next  point  of 
preliminary  interest  appears  to  be  the  subject-matter  on 
which  Proof  is  employed.  I  say  of  preliminary  interest, 
because  on  the  plan  to  be  here  adopted,  we  need  in  this 
place  attempt  to  treat  only  a  very  smaU  group  selected 
out  of  all  the  complicated  questions,  so  important  and 
so  fundamental  in  the  higher  study  of  Logic,  centering 
in  the  doctrine  of  Proposition,  or  Assertion,  or  Judg- 
ment. For  we  are  not  concerned  in  any  direct  way  with 
the  Psychology  of  either  Perception,  Thought,  Judgment, 
or  Inference  :  Proof  is  concerned  with  ready-made  Asser- 
tion only.  At  present  we  have  only  to  notice  certain 
broad  distinctions  in  kinds  of  Assertion,  with  especial 
reference  to  the  bearing  of  these  distinctions  on  the 
question  of  Proof     A  judgment  is  a  Thesis  only  when 


42  FALLACIES.  [Paet  I. 

capable  of  expression  in  intelligible  language,  and  while 
the  need  for  Proof  is  felt. 

First  in  importance  for  us  is  the  distinction  between 
Beal  and  what  may  be  called  Unreal  propositions.  The 
latter  of  these  are  insusceptible  of  Proof :  the  former  are 
its  subject-matter. 

The  name  'Unreal'  as  here  applied  to  propositions, 
is  somewhat  wider  than  what  is  usually  meant  by 
'verbal'  Usually  the  distinction  between  real  and 
verbal  is  taken  to  correspond  precisely  to  that  between 
'accidental'*  and  'essential'  propositions;  verbal  pro- 
positions being  restricted  to  mean  such  only  as  are 
taiUologous  or  identical, — those  in  which  the  Subject  f 
already  contains,  as  a  part,  at  least,  of  its  meaning,  that 
which  is  asserted  of  it  in  the  remainder  of  the  proposi- 
tion. Thus,  '  A  triangle  is  a  three-sided  figure '  is  com- 
monly given  as  a  typical  example  of  the  verbal  proposition. 
But  for  our  purposes  we  need  some  name  to  express  indis- 
criminately all  kinds  of  assertion  which  are  insusceptible 
of  Proof ;  and  in  order  to  avoid  ambiguities  I  propose  to 
call  these  '  unreal,'  rather  than  verbal.  In  itself  the  name 
'  verbal '  might  certainly  be  held  to  designate  very  appro- 
priately every  proposition  which  is  merely  a  string  of 
words,  fulfilling,  it  may  be,  all  grammatical  requirements, 
but  without  conveying  sense, — mere  empty  sound  so  far 

•  Or,  as  the  corresponding  '  Judgments '  are  termed  (by  Hamilton  and 
others),  '  Ampliative  '  and  *  Explicative,'  or  (by  Kant)  '  Synthetical '  and 
'  Analytical.' 

t  '  Subject'  we  may  define  provisionally  as  '  that  which  is  primarily 
spoken  of.'     There  will  be  more  to  say  about  it  presently. 


CiiAP.  II.]      SUBJECT-MATTER  OF  PROOF :  IN   GENERAL.        43 

as  possibility  of  interpretation  is  concerned ;  but '  verbal ' 
is  a  name  already  in  use  for  a  more  restricted  purpose. 

At  this  stage  it  is  not  necessary  to  face  the  question 
as  to  the  means  of  distinguishing  in  practice  unreal  pro- 
positions from  real.  Such  inquiry  belongs  to  a  later 
place  in  our  scheme,  and  will  there  be  to  some  extent 
discussed.*  At  present,  we  have  only  to  register  the 
fact  that  unreal  propositions  are  to  be  met  with, — empty 
shells  of  assertion  without  a  kernel, — and  to  set  out  the 
heads  under  which  these  may  be  conveniently  divided. 

In  the  first  place,  then,  comes  the  case,  already  spoken 
of,  where  the  assertion  is  already  made  as  soon  as  the 
meaning  of  the  '  Subject '  is  understood, — tautologous, 
or  essential,  or  identical  propositions.  It  is  easy  to  see 
that  where  that  which  is  said  of  a  thing  is  that  which  is 
known  already,  or  rather  that  which  is  already  told  as 
soon  as  the  Subject  is  enunciated,  the  proposition  (for  in 
form  it  may  still  of  course  be  a  proposition,  containing 
nominative  case  and  verb)  lacks,  if  not  raison  d'etre, 
at  least  capacity  for  proof.  The  mere  attempt  to  prove 
any  such  proposition  involves  a  vicious  circle  in  our 
thoughts.  We  have  prejudged  already,  by  hypothesis, 
the  question  of  its  truth,  and  inquiry  can  lead  but  to  one 
result — a  result  which  might  have  been  reached  without 
the  labour.  If,  for  example,  a  coroner's  jury  were  to  give 
it  as  their  solemn  opinion,  that  'deceased  came  to  his 
death  by  extinction  of  the  vital  forces,'  it  would  require 
no  great  efibrt  to  see  that  this  supposed  piece  of  informa- 
♦  See  pp.  120-147. 


44  FALLACIES.  [Part  I. 

tion  leaves  us  exactly  where  we  were  before.  This, 
however,  is  rather  an  extreme  instance.  Perhaps  the 
commonest  case  of  all  is  where,  in  some  shape  or  other, 
a  proposition  laboriously  informs  us  that  excess  is  not 
advisable, — as  (in  a  discussion  on  local  legislation  in  one 
of  the  Channel  Islands, — I  quote  from  a  newspaper 
report)  "  The  Bailiflf  said,  it  was  essential  that  no  measure 
should  be  unnecessarily  adopted.  On  the  other  hand, 
everything  necessary  must  be  done."  Or  again,  "  I  should 
not  advise  too  great  hurry,"  or  "Growing  lads  and 
women  should  not  attempt  too  much  at  a  time."  If '  too 
much '  means  anything  at  all,  it  means  that  on  the  whole 
the  amount  spoken  of  is  not  advisable,  and  in  all  such 
cases  no  real  information  is  given  until  the  speaker  pro- 
ceeds to  say  how  much  is  considered  by  him  excessive.* 
These  instances  are  purposely  chosen  as  being  almost 
self-evident  and  indisputable.  Later  on,t  we  shall  have 
occasion  to  notice  some  of  the  real  difficulties  in  the 
matter. 

In  the  second  place  come  the  cases  where  the  asser- 
tion made  is  already  denied  in  the  meaning  of  the  Subject 
— self-contradictory,  or  suicidal  propositions.    These,  of 

*  It  mnst  be  here  remarked,  however,  that  in  many  cases  such  asser- 
tions are  merely  blnndering  expressions,  or  grammatical  solecisms,  rather 
than  absolutely  without  a  meaning, — the  speaker  and  his  audience  both 
having  some  actual  amount  dimly  in  view.  There  are  also,  no  doubt,  a 
few  cases  where  '  too  much '  does  not  really  intend  to  sum  up  the  total 
question  of  advisability,  but  refers  to  some  other  standard,  as  in  the 
sentence,  'It  is  better  to  have  too  much  luggage  ou  a  journey,  than 
too  little.' 

t  See  p.  124,  inf. 


Chap.  II.]     SUBJECT-mXtTER  OF  PROOF :  IN  GENERAL.      45 

course,  stand  essentially  on  the  same  footing  as  the  class 
just  mentioned.  The  question  of  their  truth  is  prejudged 
already,  only  the  reverse  way.  Perspicuous  examples 
which  are  really  faulty  are  less  common  here  however, 
since  the  explanation  of  their  actual  employment  is  not 
so  frequently  as  in  the  case  of  tautology  a  slipshod, 
do-nothing,  easily  satisfied  habit  of  thought,  but  rather 
a  youthful,  reckless,  revolutionary  spirit,  making  use  of 
poetical  license  in  expression,  or  aiming  at  strong 
rhetorical  effect.  There  is  usually  more  life  in  self- 
contradictory  assertions  than  in  platitude,  even  if  it  be 
life  of  a  rather  uncurbed  nature,  and  often  these  are  used 
to  convey  in  a  forcible,  epigrammatic  manner,  real  truths 
which  may  indeed  be  paradoxical  (in  the  sense  of  being 
contradictory  to  received  opinion),  but  which  are  none 
the  less  worth  knowing  :  still,  as  they  stand,  such  propo- 
sitions take  their  place  outside  the  realm  of  Proof,  since 
in  Logic  we  are  necessarily  limited  by  language,  what- 
ever its  faults  may  be.  Luckily,  however,  an  epigram 
that  is  worth  anything  may  generally  be  translated  into 
a  real  proposition  if  we  can  be  content  to  sacrifice  its 
merely  artistic  qualities  ;  and  since  the  practical  value  of 
these  can  only  be  for  stirring  up  our  sluggish  attention, 
when  this  object  is  once  accomplished  we  may  safely 
relapse  into  a  cooler  state  of  mind.  Where  harm  is  done 
by  self-contradictory  propositions  is  not  so  much  in  the 
field  of  positive  assertion  as  in  that  of  doubt;  where, 
for  instance,  doubts  are  nominally  raised,  by  means  of 
language,  about  something  which  language  itself  postu- 


46  FALLACIES.  [Pabt  t 

lates  as  a  starting-point, — as  {e.g.)  "  Can  one  individual 
be  at  the  same  time  another  individual  ? "  Or,  "  By 
successive  additions  of  nothing,  can  something  be  at  last 
developed  ? "  No  question  here  can  exist  for  Proof,  as 
we  shall  understand  that  term,  since  the  answer  is 
given  already  in  the  postulates  of  language  (otherwise 
known  as  the  '  Maxims  of  Consistency '  or  the  '  Laws  of 
Thought'*),  and  language  is  needed  in  order  to  state 
the  question. 

This  remark  leads  us  to  the  outskirts  of  a  very  thorny 
subject, — namely  the  position  of  '  Ultimate  beliefs '  in 
regard  to  unreality.  It  may  be  said  at  once  that  they  do 
not  come  within  the  subject-matter  of  Proof  as  here 
understood.  Without  attempting  to  determine,  even 
approximately,  the  number  or  the  nature  of  these  ulti- 
mate beliefs,  or  to  say  anything  further  about  them,  it 
will  suffice  to  acknowledge  (if  required  to  do  so)  that  such 
there  must  be.  Pushing  back  the  examination  of  reasons 
for  any  belief  we  must  of  course  either  ultimately  come 
to  a  basis  of  mere  assumption,  or  go  on  questioning  for 
ever.  It  seems  best,  therefore,  at  once  to  admit  the 
existence  of  beliefs  which  may  stand  above,  and  not 
below,  the  possibility  of  'Proof;'  and  then  to  relegate 
all  discussion  of  such  beliefs  and  their  validity  to  those 
who  feel  desirous  of  examining  them,  and  competent  to 
undertake  the  inquiry.  For  us,  in  the  mere  capacity 
of  logicians,  and  not  metaphysicians,  language  limits 
thought ;  and  we  therefore  start  at  least  with  the  Postu- 
*  See  also  pp.  14,  105. 


CuAP,  II.]      SUBJECT-MATTER  OF  PROOF  :  IN  GENERAL.       47 

lates  on  which  the  meaning  of  language  depends,  dispens- 
ing with  all  attempts  to  climb  outside  or  above  them. 
Only  so  far  then  as  a  real  meaning  can  be  found  in  the 
answer  Yes  or  No  to  any  question, — a  meaning  expressible 
in  consistent  language  and  translatable,  if  need  be,  into 
terms  of  practice, — will  such  question  come  within  our 
subject-matter.  Wherever  to  doubt  any  belief, — e.g.  that 
'whatever  is,  is;*  or  that  'it  is  impossible  for  the  same 
thing  at  once  to  be  and  not  to  be ' — would  nullify  the 
postulated  meaning  of  the  language  used,  such  belief  (if 
it  can  be  called  a  belief  at  all ;  but  this  may  be  conceded 
for  the  sake  of  peace)  we  will  consider  to  lie  above  the 
possibility  of  proof.  And  wherever  this  does  not  appear 
to  be  the  case  then  the  grounds  of  the  belief  will  be 
open  to  our  examination,  even  if  for  the  purpose  of 
saving  time  or  trouble  it  may  be  also  open  to  us  to  dis- 
pense with  such  inquiry.  The  view  appears  a  tenable 
one,  and  has  been  stated  at  some  length  by  Mr.  Spencer,* 
that  certain  supposed  questions,  commonly  believed  to  be 
of  metaphysical  interest,  cannot  be  strictly  called  ques- 
tions at  all,  in  any  fruitful  sense  of  that  term :  but  since 
controversy  is  not  here  an  object,  it  seems  simpler  to  say 
that  we  choose  to  limit  our  own  inquiry  as  above. 

Thirdly  comes  the  case  where  any  term  used  in  a 
proposition  fails,  whether  through  self-contradiction  f  or 
otherwise,  to  convey  intelligible  meaning.  There  is,  so 
far  as  I  am  aware,  no  special  name  in  use  for  this  kind  of 

*  Principles  of  Psychology,  pt.  vii.  ch.  iii. 

t  i.e.  within  the  term,  not  between  the  two  terms. 


48  FALLACIES.  [Paet  I. 

unreal  assertions  as  a  class,  although  certain  forms  of 
them  have  (very  properly)  earned  the  name  of  mysteries. 
These  too,  from  the  nature  of  the  case,  may  safely  sing  in 
presence  of  the  robber  Doubt.  So  far  as  they  are  consist- 
ently incomprehensible,  so  far  the  question  of  their  truth 
or  falsity  can  clearly  not  be  raised,  except  in  words.  Their 
acceptance,  indeed,  as  a  formula,  may  show  a  willing  and 
tractable  spirit,  and  they  may  to  that  extent  have  a 
value :  but  such  acceptance  differs  of  course  from  belief 
in  being  admittedly  a  voluntary  act,  and  not  a  mere  im- 
meritorious  and  reluctant  yielding  to  the  brute  weight  of 
evidence.  Here  too  it  is  somewhat  difficult  to  find 
examples  which  shall  be  universally  perspicuous, — unless 
we  take  such  questions  as  were  sometimes  discussed  by  the 
Scholastics, — as  whether  two  glorified  bodies  can  occuj)y 
the  same  portion  of  space  at  once,  or  whether  God  knows 
more  than  He  is  conscious  of:  or  the  doctrines  of  the 
Cabbala, — that  all  souls  pre-existed  in  Adam,  that  the 
human  is  united  to  the  Divine  mind  as  the  radius  of  a 
circle  to  its  centre,  or  that  existence  is  infinitely  distant 
from  non-entity. 

Besides  assertions  which  are  thus  completely  insus- 
ceptible of  Proof,  there  are  also  many  cases  where  Proof 
may  appear  to  be  inapplicable;  which  cases  however 
must  be  carefully  distinguished  from  unreal  propositions. 
Such,  for  example,  is  the  case  where,  though  the  belief  is 
real  enough,  and  quite  possibly  sound,  proof  is  unattain- 
able owing  to  the  multitude  or  the  intangible  nature  of 
the  grounds  of  belief,  or  owing  to  the  shortness  of  the 


Chap.  II.]      SUBJECT-MATTER  OF   PROOF  :  IN   GENERAL.       49 

time  available  for  their  examination — as  where  we  take 
a  violent  liking  or  dislike  to  a  person  at  first  sight,  or 
have  to  decide  in  a  hurry  upon  some  complicated  course 
of  action.  In  such  cases  the  incapacity  for  proof — if 
there  be  real  incapacity — cannot  be  discovered  by  mere 
inspection  of  the  thesis,  but  needs  to  be  shown  by  ex- 
ternal evidence.  And  unless  and  until  this  is  shown  in 
the  given  case,  we  have  clearly  no  reason  to  treat  it 
differently  from  any  other  real  assertion. 

Under  the  head  of  propositions  insusceptible  of  exact 
proof  it  may  be  well  also  to  notice  that  immense  class  of 
assertions,  very  commonly  in  use,  whose  essential  nature 
is  to  be  vague.  Such  assertions  as  that  on  the  whole  the 
ordinary  meaning  of  a  word  is  so  and  so,  or  that  there  is 
a  growing  tendency  among  civilised  people  to  do  this  or 
the  other ;  or,  still  more,  the  finer  shades  of  suggestive, 
tentative  assertion  conveyed  in  poetry,  jest,  or  innuendo : 
these  aflford,  from  the  nature  of  the  case,  an  insecure 
footing  for  the  fruitful  application  of  logical  method. 
But  these,  too,  stand  on  a  very  different  level  from  unreal 
propositions,  since  the  reduction  of  them  to  definiteness  is 
not  in  any  way  precluded  by  their  own  postulates,  but 
only  difficult  perhaps,  or  at  any  rate  inconvenient  on 
some  ground  or  other.  When  we  meet  with  one  of  these 
assertions,  two  courses  are  open:  either  to  treat  it  in 
a  spirit  of  generosity  or  carelessness,  accepting  it  as 
claiming  only  a  lower  degree  of  assertive  force,  and  as 
fulfilling  its  own  purpose  if  not  exactly  ours ;  or  else,  if 
exactitude  be  for  any  reason  really  important,  expending 


60  FALLACIES.  [Pakt  I. 

the  trouble  necessary  to  render  it  as  far  as  possible 
definite.  Until  this  is  done  there  is  of  course  room  for 
misinterpretation,  and  therefore  no  security  for  strict 
sifting  of  the  question  raised. 

Lastly,  it  is  obvious  that  many  assertions  which  might 
be  proved,  do  not  in  fact  stand  in  need  of  it.  There  are 
a  vast  number  of  cases  in  which  Proof  is  practically  never 
demanded.  That  '  Socrates  is  mortal,'  for  example,  or 
that  'Queen  Anne  is  dead ;'  that '  some  coins  are  metallic,' 
or  some  logical  examples  rather  absurd;  these  are  assertions 
which,  for  all  practical  purposes,  may  now  be  considered 
sufficiently  safe  against  serious  attack.  Here,  too,  no 
general  rule  can  be  given  for  distinguishing  propositions 
which  have  been  sufficiently  proved  already  from  those 
which  still  stand  in  need  of  proof.  This  is  one  of  the 
matters  which  fall  quite  outside  the  scope  of  Logic,  and 
must  always  be  decided  between  the  assertor  and  his 
audience  by  special  agreement.  It  is,  in  fact,  merely  pre- 
liminary to  Logic,  and  in  no  way  connected  with  the 
actual  methods  of  Proof  To  claim  for  a  proposition,  the 
truth  of  which  is  still  highly  doubtful,  the  advantage 
which  belongs  to  one  that  has  successfully  resisted  all 
attacks,  is  no  doubt  a  common  enough  rhetorical  device. 
So,  on  the  other  hand,  is  the  attempt  to  obstruct  an 
argument  by  raising  unnecessary  difficulties.  But  Logic 
cannot  undertake  to  judge  of  motives.  Later  on,  in 
speaking  of  the  Burden  of  Proof,  we  shall  have  occasion 
to  notice  this  difficulty  more  fully.*  At  present  it  is 
*  See  pp.  154-167,  inf.,  also  pp.  128, 171. 


Chap.  II.]     SUBJECT-MATTEE  OF  PROOF :  IN  GENERAL.       61 

important  to  pass  on  to  tlie  discussion  of  Real  Assertion, 
its  nature  in  general;  and  to  a  broad  classification 
of  the  kinds  of  Real  Assertion  that  may  be  proposed 
for  Proof. 


II.  Subject  and  Predicate. 

It  is  on  all  hands  admitted  that  every  proposition,  as 
soon  as  understood,  may  be  divided  into  two  parts — the 
subject,  or  name  of  the  'thing'  primarily  spoken  of,  and 
the  remainder  of  the  sentence,  or  the  words  expressing 
the  whole  assertion  made  about  such  Subject.  If  we  de- 
note the  Subject,  as  is  usual  for  shortness,  by  the  letter  S, 
we  may  denote  the  remainder  of  the  proposition  by  the 
letter  J — the  Judgment  made  about  the  S. 

In  so  general  a  science  as  Logic — or  since  the  province 
of  Logic  is  not  yet  clearly  marked  out,  let  us  say  in  so 
general  a  science  as  that  of  Evidence,  or  Proof — we  find 
ourselves  constantly  brought  up  against  the  difficulty  of 
obtaining  words  wide  enough  to  include  all  that  we 
mean.  Thus,  though  assertion  always  asserts  'some- 
thing' of  'something'  else — though  'everything'  may 
have  assertions  made  about  it — yet  it  seems  hardly  safe 
to  say  that  assertion  is  always  about  '  things ; '  unsafe 
at  least  without  explaining  that  '  thing '  is  here  used  in 
the  widest  possible  sense.  Not  merely  every  thing  (as 
commonly  understood — namely  every  material  object) 
may  be  the  S  of  a  proposition,  but  literally  everything, 
or  anything,  that  can  be  named  at  all :  everything  that 


62  FALLACIES.  [Paet  I. 

can  be  spoken  of,  whether  objective  or  subjective,  real  or 
imaginary,  whole  or  part,  great  or  small.  The  universe 
itself  is  a  '  thing '  in  this  sense,  and  so  is  every  portion 
of  it.  Time  and  space  are  things  in  this  sense,  and  so 
is  the  year  1882,  or  the  point  of  the  pen  with  which  I 
write :  so  is  the  heat  of  to-morrow's  sun,  or  the  justice 
shown  in  my  friend's  remarks  of  yesterday :  so  is  the 
word  'Logic,'  or  the  meaning  of  that  word,  or  the 
relation  between  its  meaning  and  something  else,  or  the 
character  of  that  relation,  or  the  fact  that  the  character 
of  that  relation  is  beyond  my  power  to  state.  We  need 
some  name  thus  to  express  in  general  'anything  that 
may  be  spoken  about,'  and  in  spite  of  the  possibly  mis- 
leading associations  of  the  word  here  chosen  (which  at 
first  sight  may  seem  to  demand  tangibility  almost,  or  at 
least  visibility  or  weight)  there  is  really  no  other  name 
that  wiU  mislead  so  little.  If  we  may  say  'every- 
thing' in  one  word  shall  we  not  say  'every  thing'  in 
two  ?  At  any  rate  such  employment  of  the  word  will 
here  be  postulated,  in  default  of  any  other  name  to  serve 
the  purpose  required. 

Every  proposition,  then,  so  soon  as  understood,  may 
be  divided  into  S  and  J.  But  it  may  also  be  divided  in 
this  way  before  the  proposition  as  a  whole  is  clearly 
understood :  namely,  as  soon  as  S  alone  is  distinguished, 
and  while  the  complete  assertion  made  is  still  obscure. 
J  itself  is  subdivisible,  and  until  this  further  subdivision 
is  ready  to  be  made,  the  meaning  of  the  proposition  is 
not  yet  completely  apprehended. 


Chap.  H.]     SUBJECT-MATTER  OF  PROOF :  IN  GENERAL.       63 

Mr.  Venn,  in  his  Symbolic  Logic*  discusses  three 
distinguishable  views  of  the  import  of  propositions — the 
predication  view,  the  class  inclusion  and  exclusion  view, 
and  the  compartmental  view ;  finally  adopting  the  last 
as  best  suited  to  the  purposes  there  aimed  at,  and  espe- 
cially to  the  solution  of  intricate  artificial  problems.  But 
there  is  a  fourth  theory  which,  though  agreeing  with  the 
compartmental  view  in  one  of  the  main  points  in  which 
it  difiers  from  the  older  doctrine — namely  in  considering 
that  every  proposition  has  (at  least)  two  subjects,  each 
term  being  the  name  of  a  "  thing  spoken  about " — yet 
seems  to  me  to  differ  from  it  fully  as  much  as  the  pre- 
dication-view and  the  class-view  differ  from  each  other. 
That  theory,  suggested  in  Mill's  system,t  stated  very 
broadly  by  Mr.  H.  Spencer,J  and  more  recently  worked 
out  into  considerable  detail  by  Mr.  Carvcth  Read,§  may  be 
described  as  the  relation-\iew  of  propositions,  and  may  be 
briefly  explained  as  considering  that  every  proposition 
really  asserts  the  manner  in  which  two  'nameable 
things'  are  related  to  each  other;  e.g.  as  resembling  or 
differing,  and  to  what  extent;  as  successive  or  simul- 
taneous in  time,  or  conjoined  in  space,  and  whether 
invariably  so  or  otherwise.     For  example,  the  most  im- 

•  Chap.  i. 

t  In  spite  of  Mill's  express  adoption  of  the  predication.theory 
{Systevi  of  Logic,  bk.  i.  oh.  iv.),  yet  his  whole  view  of  'connotation,'  as 
also  of  cansal  sequence,  was  essentially  that  of  a  relation  asserted 
between  two  Subjects. 

%  Principles  of  Psychology,  part  vi.  chap.  viii. 

§  Essay  on  The  Theory  of  Logic. 
4 


64  FALLACIEa  IPabtI. 

portant  assertions  of  succession  in  time  are  those  of 
Causation, — the  effect  following  its  cause :  again,  descrip- 
tive assertions,  and  those  which  classify  the  S,  may  always 
be  viewed  as  asserting  the  conjunction  of  attributes  (in 
space  or  time  or  both), — as  when  the  attribute  *  falli- 
bility' is  said  to  be  invariably  conjoined  with  the  other 
attributes  common  to  human  nature. 

It  is  usual  in  Logic  to  divide  what  was  above  sym- 
bolised by  J  into  (1)  Copula,  and  (2)  Predicate :  and  if  it 
were  possible  to  keep  these  names  while  avoiding 
ambiguity,  I  would  gladly  do  so.  But  though  '  Copula ' 
might  fairly  be  used  to  express  'relation  asserted,'  it 
seems  impossible  to  divest  the  name  '  Predicate '  of  its 
etymological  associations,  so  as  to  view  it  as  really  the 
name  of  another  '  thing  spoken  about.'  We  must  there- 
fore here  adopt  another  symbol,  and  perhaps  the  letter  ^ 
is  as  little  ambiguous  as  any.  Under  the  relation-view 
then,  the  form  of  proposition  would  be,  not  S  copula  P, 
but  S  copula  ^. 

In  adopting  the  relation- view,  however,  it  must  by 
no  means  be  supposed  that  we  need  therefore  discard  the 
traditional  doctrine  as  erroneous.  The  predication-view 
is  useful  for  many  purposes,  and  perhaps  its  best  practical 
excuse  is  that  so  often  one  of  the  two  'things  spoken  of 
,  is  more  directly  spoken  of  than  the  other.  One  of  them 
:  forms  the  starting-point  for  the  assertion,  while  the  other 
forms  its  goal.  Thus  S  may  denote  an  observed  or  known 
event,  and  ^  its  supposed  cause  or  effect;  as  in  'This 
death  points  to  foul  play,'  or  '  The  war  will  disturb  all 


Chap.  II.]     SUBJECT-MATTER  OF  PROOF  :  IN  GENERAL.       55 

prices : '  or  S  may  be  the  name  of  something  quite 
familiar,  and  ^  one  of  its  less  obvious  causes,  conse- 
quences, or  concomitants,  or  less  familiar  names;  as  in 
'Tubercle  is  due  to  organic  germs,'  or  'Strikes  are 
ruinous  to  the  country,'  or  '  Gold  has  specific  gravity 
19'34,'  or  'Whales  are  mammals.'  Although,  in  short, 
every  relation  is,  strictly  speaking,  two-sided,  not  every 
assertion  is  concerned  equally  about  both  its  possible 
aspects.  If  S  'resembles'  ^,  for  example,  it  certainlj"^ 
cannot  be  denied  that  the  latter  also  resembles  the 
former,  and  yet  our  whole  concern  in  making  the  asser- 
tion may  be  to  bring  the  former  just  within  the  range 
of  what  we  know  (or  suppose  to  be  true)  of  the  latter ; 
our  knowledge  of  ^,  as  regards  relation  to  a  third 
term,  Z,  being  in  some  way  better  established  than  our 
knowledge  of  S.  Again,  if  S  'indicates'  ^,  the  latter 
'is  indicated  by'  the  former;  but  the  main  purpose  of 
indication  is,  of  course,  to  point  from  sign  to  thing  sig- 
nified. The  former  is  the  starting-point  and  the  latter 
the  goal. 

The  relations  that  may  exist  between  S  and  ^,  as 
thus  understood,  are  of  course  extremely  numerous. 
That  is  to  say,  we  can,  if  for  any  purpose  it  be  desirable, 
distinguish  an  endless  number  of  them.  S  may,  for  in- 
stance, be  the  father  of  ^,  or  his  mother,  child,  wife, 
etc.;  or  larger  than  ^,  or  less  ambitious,  or  may  live 
next  door  to  ^,  or  may  be  related  to  him,  or  her,  or  it,  in 
a  million  different  ways.  For  our  purpose,  however,  it 
wiU  fortunately  be  sufficient  to  make  only  the  broadest 


66  FALLACIES.  [Pabt  I. 

subdivision;  and  such  subdivision  will  be  the  subject  of 
the  next  following  chapter.  But  first  there  is  a  prelimi- 
nary source  of  difficulty  to  be  cleared  away. 


III.  Simple  and  Complex  PROPOSinoNa 

Such  propositions  as,  'All  men  are  fallible/  or  'He 
is  a  man/  are  somewhat  unusually  simple.  That  is  to 
say,  they  are  capable  of  being  expressed  in  comparatively 
few  words,  without  either  circumlocution  or  intricacy. 
There  are,  indeed,  other  propositions  still  simpler,  as  '  He 
runs/  or  'I  exist;**  but  the  majority  in  common  use 
are  of  a  much  more  complicated  nature,  each  of  the 
terms  being  frequently  made  up  of  a  large  number  of 
words,  or  even  of  a  combination  of  intricately  inter- 
woven clauses.  This  sentence  just  written,  for  example, 
is  only  moderately  advanced  in  the  scale  of  complexity, 
and  yet  considerably  more  so  than  'All  men  are  fallible:' 
any  book  or  newspaper  taken  at  hazard  will  immediately 
supply  the  reader  with  a  dozen  better  instances.  Simple 
propositions,  of  the  type  so  familiar  in  logical  text-books, 
are  quite  exceptional  in  real  life. 

From  our  point  of  view  there  is  no  firm  line  to  be 
drawn  between  simple  assertions  and  complex  ones. 
That  is  to  say,  so  soon  as  we  distinguish  the  terms  of 
any  proposition,  no  matter  how  complex  in  verbal  form, 

*  For  the  manner  in  which  propositions  asserting  mere  existence  of 
the  S  may  be  viewed  as  stating  a  relation  between  Uoo  terms ;  see  Bain's 
Logic,  book  i.  chap.  iii.  §  23. 


Chap,  n.]     SUBJECT-MATTER  OF  PROOF  :  IN  GENERAL.       57 

we  thereby  simplify  it  into  one  assertion.  The  mere 
fact  that  a  given  set  of  words  can  be  viewed  as  com- 
prising two  assertions  coupled  by  a  'conjunction/  does 
not  necessarily  prevent  us  from  taking  the  two  together 
and  considering  their  joint  intention.  Still  less,  of  course, 
do  mere  dependent  clauses,  or  adjectival  or  adverbial 
limitations,  destroy  the  unity  of  meaning.  The  com- 
monest type,  perhaps,  among  propositions  is  that  where 
the  terms  each  consist  of  some  main  constituent,  limited 
or  qualified  in  several  ways.  It  is  rarely  that  we  have 
the  opportunity  of  making  a  perfectly  simple  statement 
about  a  '  thing '  which  can  be  expressed  by  a  perfectly 
unqualified  name, — as  'man'  or  'humanity:'  we  find 
it  safer  as  a  rule  to  confine  the  extent  of  our  assertions 
somewhat,  and  thus  we  render  them  complex  in  form. 
There  are  comparatively  few  statements  that  we  can 
make  with  any  safety  about  '  All  men,'  except  such  as 
are  already  too  familiar  to  be  much  required:  but  we 
may  often  find  occasion  to  speak  of  'All  men  who 
possess  such  and  such  a  peculiarity,'  or  '  All  except  those 
who,  etc.,'  whereby  our  sentence  becomes  more  complex 
and  the  assertion  more  limited  in  range. 

It  will  not  be  necessary  here  to  make  any  division 
of  propositions  in  order  to  show  the  different  kinds  of 
complexity  to  which  they  are  liable.  Such  a  question  is 
altogether  more  of  grammatical  interest  than  logical,  and 
has  certainly  no  importance  for  any  purpose  here  under- 
taken. As  will  be  seen  later,  we  postulate  agreement 
as  to  meaning,  as  a  starting-point  for  Proof,  declining  all 


58  FALLACIES.  [Part  t 

invasion  of  the  grammarian's  province  by  any  attempt 
to  decide  authoritatively  what  any  given  form  or  set  of 
words  shall  imply.  But  it  seemed  necessary  to  make 
clear  from  the  outset  that  the  number  of  words,  or  of 
phrases  anyhow  combined,  is,  in  our  view,  in  itself  no 
bar  to  the  whole  group  being  regarded  as  one  assertion. 
Thus  (e.g.)  the  complex  assertion,  '  He  is  fallible,  for  he 
is  a  man,'  besides  being  capable  of  being  viewed  as  tivo 
propositions  set  in  relation  to  each  other  by  a  conjunctive 
particle,  is  also  capable  of  being  viewed  as  itself  one 
whole  proposition ;  *  i.e.  as  being  divisible  into  two  terms 
set  in  relation  to  one  another  by  means  of  a  copula.  But 
this  will  appear  more  clearly  in  due  course. 

•  See  also  pp.  34i,  100,  310,  below. 


CHAPTER  lit 

THE  SUBJECT-MATTER  OF  PROOF  :   MAIN  KINDS  OF 
THESIS. 

I  Indication. 

The  most  general  of  all  relations,  asserted  or  denied, 
is  that  which  for  want  of  a  better  name  may  in  the 
meantime  be  called  'Indication.'  The  copula  'indicates,' 
as  here  understood,  includes  the  copula  '  is '  (as  in  '  S  is 
P '),  stretching,  however,  beyond  the  usual  interpretation 
of  the  latter.  By  calling  this  the  most  general  relation 
it  is  meant  that,  with  the  one  doubtful  exception  of  the 
purely  quantitative  relations  (the  laws  of  which  are  amply 
developed  in  Mathematics,  and  require  notice  only  in  a 
more  comprehensive  scheme  than  can  here  be  attempted), 
every  proposition  may  be  viewed  as  saying  that  one 
thing '  indicates,  or  does  not  indicate,  a  certain  other. 

The  apparent  rashness  of  this  statement  will  serve  at 
least  to  show  where  the  difficulty  lies.  Some  word  is 
wanted,  for  the  purpose  of  generalising,  in  one  expression, 
several  kinds  of  assertion  which  are  commonly  described 
by  different  names ;  no  word  appears  to  me  to  be  better 


60  FALLACIES.  [Pabt  I. 

suited  for  the  purpose  than  '  indicates,'  and  yet  even  this 
would  certainly  not  be  sufficient  without  some  explana- 
tion. By  means  of  the  symbol  — >,  indeed,  it  is  possible 
to  avoid  ambiguity,  but  since  the  symbol  must  have  a 
name  we  cannot  altogether  escape  the  use  of  language, 
and  can  only  strive  while  using  it  to  avoid  any  misleading 
associations. 

For  the  purpose  of  dealing  with  the  dangers  of  Proof, 
— including  thereunder  all  dangers  to  which  a  thesis,  or 
asserted  judgment,  is  liable, — the  most  important  fact 
about  propositions  seems  to  be  the  power  which  they 
give  us  (when  their  truth  is  believed)  of  passing  from 
the  known  to  the  unknown.  There  are  two  distinct 
ways  in  which  they  may  do  this,  one  of  which  may  be 
called  *  implication,'  *  and  the  other  '  material  indica- 
tion;* the  former  being  the  case  where  by  merely 
analysing  the  meaning  of  a  name  or  proposition  we 
either  arrive  at  or  guarantee  certain  of  its  less  obvious 
consequences;  while  'indication'  (in  general)  includes 
this  case  and  also  the  commoner  one  where  we  obtain 
the  same  power,  not  by  mere  analysis  of  the  meaning,  but 
by  viewing  one  fact  as  material  evidence  for  another, 
— evidence  asserted  as  strong  enough  to  stand  against 
all  hostile  criticism.  The  proposition  'Man  is  fallible' 
might  be  an  instance  of  either  of  these  modes  of  indica- 

•  Cf.  Mr.  H,  MacColl,  in  Mind,  No,  xvii.  p.  45.  The  difference 
between  Mr.  Mao  Coil's  yiew  and  mine  appears  to  me  far  less  important 
than  the  resemblance ;  and  I  trace  much  of  my  own  view  (and  especially 
the  '  law  of  counter-indication ')  jointly  to  the  article  quoted,  and  to 
Wundt's  recent  work  (Jjogik,  vol.  i.  Erkenntnisslehre). 


Chap.  UL]  MAIN  KINDS  OF  THESIS.  CI 

tion,  according  as  the  notion  '  fallibility  *  did  or  did  not 
enter  into  the  special  meaning  postulated  for  the  name 
*  man.'  If  we  pass  to  '  new  knowledge '  *  by  analysing 
the  old,  we  do  not  reach  a  new  theory,  but  the  applica- 
tion of  an  old  one :  while  the  attempt  to  prove  by  way  of 
implication  is,  of  course,  either  to  argue  in  a  circle  or  to 
appeal  ad  hominem.  Material  indication  is  the  sole 
means  of  really  passing  from  unknown  to  'theorised,' 
or  from  theorised  to  known, — so  far  as  knowledge  is 
capable  of  being  guaranteed. 

The  chief  difficulty  about  the  name  'indication'  consists 
in  stretching  it  to  cover  the  assertion  of  both  Law  and 
Fact;  or,  as  such  assertions  will  here  be  called.  Abstract 
and  Concrete  propositions.  It  is  easy  enough  to  see  how 
every  Laiv  asserted  may  be  viewed  as  an  indication,  since 
the  primary  purpose  of  every  law  is,  of  course,  to  be  in- 
terpreted, or  applied :  hence  the  S  of  every  abstract  pro- 
position is  expressed  either  directly  as  a  '  general  name  ' 
(simple  or  complex),  or  else, — and  especially  where  such  S 
is  itself  a  proposition — is  generalised  by  means  of  an  '  if,' 
or  '  where,'  or  '  when,'  etc.  But  when  we  come  to  speak 
of  concrete  propositions,  the  word  *  indicates '  draws  us 
at  once  into   clumsiness  of  expression.      This  case  of 

•  The  question  whether,  by  analysis  merely,  we  can  "  increase  our 
knowledge "  is  as  ambiguous  as  the  question  whether  by  digestion  we 
can  "  increase  "  the  food  we  swallow.  We  do  not  increase  its  sum,  or 
weight :  we  do  increase  its  utility.  We  get  a  new  and  firmer  grasp  of 
old  material.  Though  we  may,  of  course,  add  to  our  power  of  applying 
knowledge,  by  analysing  accepted  truths,  this  merely  points  to  the 
thoughtlessness  with  which  we  habitually  bolt  our  axioms  whole. 


62  FALLACIES.  [Part  I. 

death,  no  doubt,  may  indicate  (or  point  to)  poison,  or  my 
pulse  at  the  present  moment  may  indicate  (or  show)  the 
absence  of  fever,  or  yesterday's  panic  in  the  city  may 
indicate  (or  foreshadow)  a  future  increase  of  bankruptcy ; 
but  it  is  undoubtedly  clumsy  to  say  that  Bavius  '  indicates 
the  qualities  of  a  fool:  we  habitually  condense  those 
four  words  into  the  one  word  '  is.' 

Nevertheless,  with  this  apology,  I  propose  to  use  the 
name  'indicates'  in  default  of  a  better  to  fit  all  cases. 
Much  of  the  difficulty  may  be  removed  by  remembering 
that  it  is  only  in  abstract  propositions  that  S  is  really  a 
sign,  in  the  ordinary  sense  of  the  term :  it  is  only  there 
at  least,  that  it  is  intended  to  be  used  as  a  sign,  or  mark, 
or  label,  bearing  a  recognised  meaning.  The  essential 
characteristic  of  concrete  propositions  is  that  their  S 
cannot  be  said,  in  general  (i.e.  universally)  to  indicate 
the  ^,  except  by  virtue  of  all  the  .special  circumstances 
bound  up  along  with  the  thing  most  prominently  denoted 
there  as  'S.'  It  may,  indeed,  be  on  general  grounds 
only  that  we  believe  this  or  that  concrete  proposition, — 
as,  that  *  the  panic  will  increase  the  number  of  failures : ' 
but  this  does  not  appear  in  the  statement.  In  the  con- 
crete proposition  we  distinctly  assert  the  possession  of 
something  over  and  above  mere  general  grounds,  namely 
a  full  review  of  all  the  special  circumstances.  In  spite  of 
any  hidden  facts,  we  assert  our  judgment  as  deserving  of 
belief. 

The  assertions  which  are  thus  to  be  included  under 
the  symbol  — >  (which  may  be  read  '  indicates ')  are 


Chap.  III.]  MAIN  KINDS  OF  THESIS.  63 

accordingly  those  o{  Dependence  *  (whether  causal  or 
logical)  and  of  Classification.  By  an  assertion  of  causal 
dependence  is  meant  an  assertion  that  two  'things,' — 
usually  events,  but  sometimes  objects  or  qualities, — are 
causally  connected  so  that  one  of  them  is  to  some  extent 
an  indication  of  the  other,  whether  a  sign  in  the  strict 
sense,  or  merely  a  symptom.  Some  '  things '  in  nature 
are  found,  or  supposed,  to  be  marks  or  signs  of  others, 
as  a  falling  barometer  indicates  a  coming  storm,  or  as 
breathing  indicates  that  life  is  not  extinct,  or  as  every 
existing  human  being  indicates  the  prior  existence  of 
a  pair  of  human  parents.  The  statement  of  these  indica- 
tions may  accordingly  be  written :  *  Falling  barometer 
— >  coming  storm,'  '  Breathing  — >  presence  of 
life'  and  'Human  being  — >  prior  human  parents.' 
By  an  assertion  of  logical  dependence  is  meant  an  asser- 
tion, that  the  truth  of  one  proposition  '  follows  from ' 
that  of  another,  or  that  the  meaning  of  one  name  is 
included  in  that  of  another.  Most  names  and  propositions 
are  intended  to  bear  a  meaning, — that  is,  to  mark  or 
signify  notions  or  facts,  —  and  some  propositions  are 
intentionally  put  forward  as  guaranteeing  the  truth 
of  others.  Thus  the  name  'Intolerance'  may  be  in- 
tended to  include  the  notion  'active  hostility;*  or  the 
assertion  '  He  is  coming,'  the  fact '  He  is  not  here ; '  or 
again,  the  assertion  '  He  is  a  man '  may  be  employed  to 
guarantee  the  truth  of  the  assertion  '  He  is  fallible.'  And 
these   may   respectively   be   written  'Intolerance  — > 

•  Cf.  Wnndt.    Logik :  Erkenntnisslehre,  pp.  179-186,  277,  281,  etc. 


64  FALLACIES.  [Pabt  I. 

active  hostilitjV  'He  is  coining  — >  he  is  not  here' 
(but  of  this  the  usual  grammatical  form  would  be  '  If,  or 
since,  he  is  coming  he  is  not  here/)  and  *  He  is  a  man 
— >  he  is  fallible '  (or  *  He  is  a  man,  and  therefore  he 
is  fallible ; '  or  *  He  is  fallible,  for  he  is  a  man.')  By  an 
assertion  of  Classification  is  meant  the  extremely  frequent 
cases  where  a  *  thing '  is  said  to  deserve  a  certain  name, 
or  to  bear  '  essential  resemblance '  to  another  thing,  or 
to  belong  to  a  certain  class,  or  to  possess  a  certain  quality, 
or  to  have  another  thing  'coexisting'  with  it;  as  in 
'Gold  is  an  elementary  substance,'  or  'belongs  to  the 
class  elements,'  or  '  The  State  essentially  resembles  a 
family,'  or  '  Every  rose  has  its  thorn '  (or '  With  every 
rose  a  thorn  co-exists ') ;  which  may  accordingly  be 
written  'Gold  — >  Element,'  'State  — >  Family,' 
'  Rose  — >  Thorn.' 

II.  Affirmation  and  Denial. 

Indication  may  be  either  afiirmed  or  denied.  Certain 
propositions,  instead  of  committing  the  assertor  to  any 
definite  statement  of  the  relation  between  S  and  ^, 
are  content  to  say  merely  that  some  definite  assertion, 
taken  as  already  made  about  them,  is  untrue.  These 
will  be  called  Denials :  all  others  will  be  called  positive 
Assertions,  or  '  Affirmations.' 

It  is  a  matter  of  some  difficulty  to  mention  any 
special  grammatical  form  as  fairly  representative  of  the 
denial,  since  even  sentences  containing  the  negative 
particle  'not,'  in  close  connexion  with  the  verb,  or  the 


Chap.  IUJ  MAIN  KINDS  OF  THESIS.  65 

quantification  '  no  *  before  a  noun,  or  a  '  negative  name ' 
as  P  (or  ^),  are  very  frequently  used  to  express  a  posi- 
tive assertion  as  here  defined.  Thus  we  may  say,  *  That 
is  not  bad,'  or  'No  pen  can  attempt  to  describe  the 
scene,'  or  '  He  is  unskilful,  worthless,  disagreeable,  incom- 
petent, etc.,'  without  at  all  attempting  to  confine  our- 
selves to  bare  denial  of  something  either  actually  or  only 
presumably  said  before.  The  grammatical  form  of  the 
proposition,  though  often  useful  as  a  hint  towards  the 
meaning  in  this  respect,  is  at  best  an  uncertain  guide ; 
nor  can  even  the  whole  context  be  taken  as  in  every  case 
complete  evidence  of  the  real  intention. 

The  two  distinct  intentions  do,  however,  exist,  and 
are  to  some  extent  inferrible  from  the  words  employed. 
Where  the  intention  is  doubtful,  there  is  nothing  to  fall 
back  upon  except  an  express  declaration  by  the  speaker 
as  to  the  sense  in  which  the  proposition  is  put  forward. 
At  present,  however,  we  are  not  concerned  with  the 
means  of  arriving  at  the  intention,  but  only  with 
classifying  those  distinguishable  meanings  which  have 
importance  for  the  doctrine  of  Proof.  Of  these  the 
most  important  is  the  distinction  between  positive 
assertion  and  bare  denial.  And  having  called  attention 
to  this  fact,  we  may  proceed  at  once  to  examine  more 
in  detail  the  manner  in  which  this  distinction  runs 
across  the  othera 


66  FALLACIES.  [Pabt  L 

III.  Abstract  and  Concrete  Propositions. 

Next  in  importance  is  the  opposition  between  Law 
and  Fact  asserted;  or,  as  it  may  be  otherwise  called, 
between  Abstract  and  Concrete  propositions.* 

The  abstract  proposition  may  be  expressed  indiffer- 
ently in  any  one  of  various  grammatical  forms,  of  which 
perhaps  the  commonest  are  those  familiar  types  (denoted 
under  the  traditional  scheme  by  the  letters  A  and 
E)  whose  S  is  the  name  of  the  members  of  a  class, 
'  All '  or  '  None '  of  whom  '  are '  P.  Thus,  '  All  men  are 
fallible'  (A),  or  'No  men  are  secure  against  fallacy' 
(E),  are  simple,  straightforward  examples  of  the  asser- 
tive abstract  proposition.  In  both  cases  the  attribute 
'humanity,'  wherever  found,  is  said  to  indicate  the 
attribute  'liability  to  error.'  Another  common  form 
which  the  abstract  proposition  takes,  is  where  the  S  con- 
sists of  what  is  sometimes  loosely  called  an  'abstract 
name,'  as  '  honesty '  or  '  theft.'  Thus,  we  might  assert 
that  '  Honesty  is  the  best  policy,'  or  that  '  Theft  cannot 
prosper  long;'  meaning,  in  the  two  cases  respectively, 
something  rather  more  clumsily  expressible  by '  Honest 
actions,  in  general,  indicate  success  as  likely  to  follow,' 
and  'Dishonest  actions,  in  general,  indicate  that  (in 
spite,  it  may  be,  of  temporary  success)  ultimate  failure 
is  probable.'  Of  course,  these  and  similar  sentences 
may  contain  other  meanings  also — may  even  be  used 

•  C/.  also  "  noticEal "  and  "  real "  propositions  in  Newman's  Qrammar 
of  Assent,  p.  7. 


Chap.  III.]  MAIN  KINDS  OF  THESIS.  67 

ironically, — but  in  so  far  as  they  are  used  to  express 
the  meaning  explained,  to  that  extent  they  are  what 
we  here  call  assertive  (or  affirmative)  abstract  proposi- 
tions. Again,  the  adverbs  'always'  and  'never*  are 
very  largely  used  to  express  the  copula  of  assertive 
abstract  indication,  as  in  'Bread  always  falls  upon  the 
buttered  side,'  or  '  A  story  never  loses  by  re-telling.'  And 
again,  another  still  commoner  grammatical  form  in  use 
is  the  conditional  or  hypothetical  sentence,  beginning 
with  '  if,'  or  '  when,'  or  '  where,'  or  '  while,'  etc. ;  as  in 
*  If  it  rains  in  Ceylon,  it  pours,'  or  '  When  poverty  comes 
in  at  the  door,  love  flies  out  of  the  window,'  or  '  Where 
there  is  smoke  there  is  fire,'  or  '  While  there  is  life,  there 
is  hope : '  in  each  of  these  cases  the  purpose  of  the 
proposition  may  be  to  assert  of  one  'thing'  that  it 
universally  indicates  another,  whether  in  the  past, 
present,  or  future,  relatively  to  itself  We  need  not  at 
present  follow  these  grammatical  variations  into  further 
detail :  enough  has  been  said  to  illustrate  them  in  a  rough 
preliminary  manner. 

The  concrete  proposition,  on  the  other  hand,  contents 
itself  with  a  less  (apparently)  sweeping  assertion.  It  says, 
not  that  S  wherever  found  indicates  ^,  but  that  in  this 
particular  instance  it  does  so.  Looking  at  all  the  cir- 
cumstances the  present  dearness  of  money  indicates  a 
coming  panic,  the  circumstances  of  this  man's  death  point 
to  some  kind  of  poison,  the  latest  political  movement 
indicates  dissension  in  the  cabinet,  or  deserves  the  name  of 
revolutionary  or  reactive,  or  whatever  else  it  may  be. 


68  FALLACIES.    '  [Pabt  L 

The  difference  is  perhaps  best  expressible  by  saying  that 
while  in  the  abstract  assertion  S  is  spoken  of  (but  by  no 
means  really  conceived)  apart  from  any  circumstances 
which  may  serve  to  individualise  it,  in  the  concrete 
assertion  the  reverse  is  the  case  :  we  here  say  that  talcing 
all  special  circumstances  into  account,  this  S  indicates 
§^,  It  is  true  that  to  every  concrete  fact  of  causation 
there  must  correspond  a  law,  if  we  can  discover  it ;  but, 
practically,  most  laws  abstract  more  or  less  from  the 
circumstances  of  the  concrete; 

Corresponding  to  abstract  assertions  there  are  abstract 
denials ;  and  of  these,  two  kinds  may  be  distinguished. 
Sometimes  we  deny  a  law  by  asserting  that  there  are 
exceptions  to  it ;  sometimes  (e.g.  frequently  in  classifying 
or  name-giving  propositions)  by  asserting  that  it  totally 
fails;  or,  in  other  words,  that  'some  difference  exists 
between  S  and  ^.'  The  former  kind  of  denial  may  be 
called  exceptive;  the  latter  an  assertion  of  difference. 
For  the  copula  in  exceptive  propositions  we  shall  hence- 
forth use,  on  occasion,  the  symbol  |  >,  and  for  assertions 
of  difference  the  symbol  z*^. 

As  to  exceptive  denials,  perhaps  the  most  frequent 
grammatical  form  which  these  take  is  that  known  under 
the  traditional   arrangement  as  the  '  particular '  *  pro- 

*  Cf.  Symbolic  Logic,  chap.  vii.  p.  161.  The  particular  proposition,  as 
actually  employed,  no  doubt  eerves  several  other  purposes  also,  notably 
that  of  registering  our  first  vague  grounds  of  Inference,  as  contrasted 
■with  anything  deserving  the  name  of  grounds  of  Proof.  Finding  two 
'  things '  frequently  or  even  occasionally  conjoined,  we  often  begin  to 
get  upon  the  track  of  some  law,  and  eventually  we  may  rise  thereby  to 


Chap.  HI.]  MAIN  KINDS  OF  THESIS.  69 

position  (I  or  O) :  e.g.  '  Some  negroes  are  fairly  intelli- 
gent/ or  '  Some  Mexicans  are  not  habitual  liars.'  Again, 
the  adverbs  '  sometimes '  or  *  sometimes  not '  are  fre- 
quently used  in  exceptive  denials ;  and  again  the  expres- 
sions *  ^  is  quite  compatible  with  S,'  or  '  S  is  by  no 
means  necessarily  ^ ;  *  and  again,  the  expression  *  all 
.  .  .  are  not,'  as  in  'All  that  glitters  is  not  gold,'  and 
various  other  forms,  such  as,  for  example,  'There  are 
lawyers  and  lawyers.'  Here  also  no  form  of  words  is  by 
itself  perfectly  unambiguous :  we  need  something  else  to 
show  whether  the  proposition  is  really  intended  as  asser- 
tive or  as  a  bare  denial.  But  on  the  whole,  and  roughly, 
the  particular  proposition  may  be  taken  as  most  nearly 
typical  of  this  class.  No  useful  distribution  of  any 
proposition  into  its  component  parts,  it  must  be  remem- 
bered, can  ever  be  made  until  the  real  intention  of  the 
speaker  is  clear. 

As  to  *  assertions  of  difference,'  there  is  some  difficulty, 
as  the  name  chosen  may  help  to  show,  in  placing 
them  quite  clearly  in  the  class  of  mere  denials.  The 
justification  for  doing  so  lies,  however,  in  the  fact  that 
without  some  supposed  belief  that,  for  the  purpose  in 
hand,  no  difference  exists  {i.e.  that  S  — >  ^)  the  asser- 
tion of  difference  is  too  trivial  to  have  any  practical 
value,  since  points  of  difference  may  always  be  found 
between  two  things,  however  nearly  alike.     Hence  the 

the  power  of  making,  and  perhaps  proving,  some  abstract  assertion 
regarding  them.  But,  regarded  as  positive  assertion,  this  is  too  vague 
to  bo  called  a  '  thesis.' 


70  FALLACIES,  [Part  L 

essential  purpose  of  these  assertions  is  to  contradict  some- 
thing already  supposed  to  be  believed.  The  sole  practical 
use  of  the  assertion  of  difference  is  either  to  break  down 
a  supposed  analogy  or  to  deny  the  applicability  of  a  name, 
i.e.  the  right  of  a  '  thing '  to  belong  to  a  certain  class ; 
and  this  whether  the  proposition  be  abstract  or  concrete. 
Thus  we  might  say  *  National  Government  is  a  different 
thing  from  family  government'  (abstract),  or  'Whales 
are  not  fishes  '  (abstract),  or  '  The  Kilmainham  arrange- 
ment was  not  a  compact '  (concrete),  or  *  The  case  of  !Mr. 
A.  is  different  from  that  of  Mr.  B.'  (concrete).  These 
propositions  merely  say  that  S  differs  from  ^.  For 
further  examples  of  this  form  of  denial  we  may  take  such 
expressions  as  '  Seeing  is  a  very  different  thing  from 
believing,'  or  'Liberty  is  one  thing  and  License  quite 
another,'  or  even  perhaps  '  Force  is  no  remedy ' ;  though 
this  last  phrase  has  no  doubt  been  more  often  used  to 
express  a  vague  law  that '  Force  — >  probable  continu- 
ance of  the  evil '  than  merely  to  deny  an  assertion  to  the 
contrary  or  to  correct  the  use  of  a  name.  As  this  last 
example  may  serve  to  show,  there  is  sometimes  a  difficulty 
in  deciding  whether  a  given  sentence  is  really  an  asser- 
tion that  S  indicates  the  absence  of  something  (as  ice,  for 
instance,  indicates  the  absence  of  a  certain  degree  of  heat), 
or  a  mere  assertion  of  difference  between  S  and  ^.  But 
this  is  a  difficulty  which  cannot  be  remedied  by  simply 
refusing  to  notice  it.  The  possibility  of  misunderstand- 
ing the  real  intention  of  a  given  set  of  words,  is  one  that 
can  hardly  too  often  be  brought  to  mind. 


Chap.  HI.]  MAIN  KINDS  OF  THESIS.  71 

Corresponding  to  concrete  assertions  there  are  con- 
crete denials;  and  of  these  again  two  kinds.  We  have 
already  spoken,  just  above,  of  the  concrete  assertion  of 
difference,  and  after  what  has  been  said  of  assertions  of 
difference  in  general,  the  nature  of  the  first  kind  of  con- 
crete denial  will  be  sufficiently  clear.  Nor  is  there  much 
difficulty  as  to  the  other  kind  of  concrete  denial.  It 
follows  from  the  nature  of  concrete  assertion  that  these 
cannot  be  at  all  described  as  '  exceptive/  since  there  is  no 
law  to  which  they  directly  take  exception.  Perhaps  the 
best  name  for  them  is  'Simple  denials.'  These  also  are 
found  in  various  grammatical  forms,  but  the  commonest 
is,  no  doubt,  where  'not'  is  added  to  the  verb,  as  in 
'  This  was  not  due  to  drink/  '  The  crisis  will  not  be  fol- 
lowed by  any  important  change/  '  It  is  not  accompanied 
by  much  danger,  after  all,'  etc.  Also  in  this  sense  a  nega- 
tive name  as  ^  may  be  sometimes  used,  though  perhaps 
rarely.  Thus  in  saying  'The  door  is  unfastened,'  we 
might  conceivably  intend  merely  to  deny  the  opposite 
assertion,  but  more  probably  the  intention  would  be  to 
convey  a  positive  assertion  of  our  own.  When  once  the 
distinction  between  concrete  and  abstract  propositions  is 
clearly  kept  in  view  it  becomes  sufficiently  easy  to  recog- 
nize the  simple  concrete  denial. 

The  abstract  proposition  is,  then,  the  assertion  or 
denial  of  any  general  law  in  Nature,  of  however  narrow 
sweep  or  insecure  stability :  the  concrete  proposition 
is  the  assertion  or  denial  of  a  single  fact.  The  con- 
crete proposition  takes  a  concrete  S,  '  this  man/  *  these 


72  FALLACIES.  [Pabt  I. 

instances,'  'my  lecture  yesterday,'  'your  hope  of  suc- 
cess '  and  tells  us  what  these  '  indicate,'  forwards  in  time, 
or  backwards,  or  contemporaneously.  And  here  must  be 
noticed  an  objection  which  may  possibly  be  raised  at  first 
sight  to  this  use  of  the  word  '  concrete.'  A  man,  it  may 
be  said,  is  clearly  concrete  enough,  and  so  perhaps  is  an 
instance ;  but  a  lecture,  is  not  that  dangerously  near 
the  abstract  ?  And  '  Hope,'  '  Success,'  are  not  these 
purely  abstract  terms  ?  The  answer  is  that  no  word 
(when  used  in  a  proposition — and  it  is  only  when  so  used 
that  we  are  here  concerned  with  words)  is  in  itself  either 
abstract  or  concrete,  but  its  context  makes  it  so.  Any 
word  may  be  either,  according  to  the  purposes  of  our 
assertion.  We  may  speak  of  '  man '  or  of  '  men '  in  the 
abstract,  in  spite  of  the  solid  flesh  belonging  to  each 
individual ;  and  on  the  other  hand,  by  hedging  in  a  so- 
called  '  abstract  name,'  with  the  help  of  a  demonstrative 
pronoun,  or  in  whatever  way  the  resources  of  language  will 
allow  us  to  apply  such  name  to  some  actual  concrete  case, 
we  destroy  for  the  time  its  abstract  nature,  and  the  pro- 
position as  a  whole  becomes  concrete.  If  I  make  an 
assertion  regarding  the  '  truth '  of  some  particular  story, 
I  state  no  law,  and  deny  no  law,  but  confine  my  remarks 
to  one  particular  concrete  fact.  The  underlying  meaning 
of  '  abstract '  is  always  '  detached  from  special  circum- 
stances,' or  '  generalised ; '  and  so  long  ago  as  Berkeley's 
time  our  limitations  in  conceiving  (or  having  a  definite 
idea  of)  anything  in  the  abstract  have  been  clearly 
shown.    We  cannot  conceive  things  in  the  abstract,  but 


Chap.  UL]  MAIN  KINDS  OF  THESIS.  73 

we  can  make  abstract  assertions  regarding  them; — can 
sometimes  say,  that  is,  how  they  will  behave  or  how 
they  should  be  explained  or  designated  under  all  cir- 
cumstances indifferently ;  and  where  we  speak  of  this 
man,  your  hope,  etc.,  we  include  special  circumstances 
which  *  man '  and  '  hope '  by  themselves  would  lack.  In 
the  concrete  proposition  we  sum  up  the  total  circum- 
stances, taking  (or  rather  professing  to  take)  all  the  indi- 
vidual peculiarities  of  the  case  into  consideration  before 
pronouncing  judgment.  Whether  or  not  'hope'  in  the 
abstract  may  tell  flattering  tales  habitually,  we  say  that 
taking  all  the  present  circumstances  into  account  it  does 
so  here.  The  S  of  a  concrete  proposition  differs  from  that 
of  the  corresponding  abstract  one  in  being  saddled  with 
all  the  individual  peculiarities  of  the  given  case.  And 
on  this  account  the  concrete  assertion  differs  from  the 
abstract  one  in  being  less  easy  to  disprove ;  since  the 
'  circumstances '  are  nearly  always  wide  enough  to  contain 
something  that  even  science  fails  to  reckon. 

It  must  now  be  sufficiently  evident  also  that  so  long 
as  the  meaning  is  clear,  the  grammatical  form  of  the 
sentence — categorical  or  hypothetical,  simple  or  com- 
plex, A  or  E,  etc. — is  not  of  the  slightest  importance. 
The  proposition,  for  instance,  'Murder  will  out,'  is,  for 
purposes  of  proof,  the  same  whether  expressed  in  this 
fashion  or  in  the  shape  'All  murders  are  eventually 
discovered,'  or  'No  murders  remain  undiscovered,'  or 
'Murder  always  comes  to  light,'  or  'Murders  never 
remain  hidden,'  or  '  When  (or  if)  murder  is  committed. 


74t  FALLACIES.  [Pabt  I. 

detection  is  sure  to  follow/  or  in  whatever  way  it  may 
suggest  itself  to  rhetorical  ingenuity  to  clothe  the  same 
meaning.  At  the  root  of  all  abstract  propositions  lies 
the  formula — 

S  (universally)  — >  ^ 
and  this  whether  ^  be  past,  present,  or  future  relatively 
to  S  and  whether  the  name  of  either  be  positive  or 
negative.  In  each  case  S  (in  general)  is  said  to  be  a 
sign,  or  mark,  of  ^,  whether  in  the  past,  present,  or 
future,  relatively  to  itself  Where  S  is  found,  ^  (it 
is  asserted)  may  be  looked  for. 

Abstract  propositions  play  an  important  part  in 
proof, — whether  proof  of  other  abstract  propositions  or 
of  concrete  ones.  They  summarise,  in  a  compact  and 
convenient  form,  whatever  general  knowledge  of  nature 
we  have  already  obtained,  and  serve  as  tests  to  which 
to  bring  any  new  assertion  propounded  for  proof.  The 
establishment  of  these  is  of  course  the  centre  of  interest 
for  science.  It  is  through  the  existence  of  such  'de- 
pendences' that  all  explanation  and  prediction  become 
possible,  and  our  consistent  recognition  of  them  consti- 
tutes the  main  difference  between  our  conception  of 
Nature  as  a  network  of  uniformities,  and  the  earlier 
notion,  so  inevitable  to  savages,  of  a  world  governed  by 
caprice  or  luck. 

Concrete  propositions,  on  the  other  hand,  although 
constituting  in  one  sense  the  foundation  for  science,  find 
their  main  interest,  as  subject-matter  for  proof,  in  a  less 
exalted  region.     Although  in  common  life  also  the  truth 


Chap.  Ill]  MAIN  KINDS  OF  THESIS.  75' 

of  general  laws  (more  or  less  vague  perhaps  in  their 
statement)  may  to  no  small  extent  be  debated,  yet  the 
bulk  of  the  questions  arising  there  for  settlement  are  of 
a  concrete  character;  and,  roughly  speaking,  the  com- 
moner the  life  the  more  relatively  frequent  are  the 
concrete  assertions  put  forward.  Whether  this  or  that 
thing,  person,  or  definite  group,  did  act  in  such  and 
such  a  manner,  or  does  possess  such  and  such  qualities ; 
whether  this  or  that  individual  action,  event,  or  '  acci- 
dent' was  due  to  such  and  such  causes,  or  will  have 
such  and  such  results ;  these  are  the  most  frequent  ques- 
tions about  which  in  daily  life  doubt  arises,  and  which 
press  for  settlement  and  proof  Every  one  of  these  is 
concrete, — an  assertion  directly  regarding  individual 
fact,  not  general  law, — and  as  such  is  marked  off  by  a 
chasm  as  wide  as  any  that  can  be  made  in  Logic,  from 
the  propositions  above  defined  as  abstract.  Between 
concrete  and  abstract  knowledge,  however,  with  respect 
to  their  attainment  and  growth,  there  has  been  mutual 
aid  and  mutual  criticism  so  far  back  as  can  be  traced  at 
all.  No  doubt,  in  one  sense,  concrete  knowledge  (or  some- 
thing separated  from  '  knowledge '  only  by  imperceptible 
degrees)  is  earlier  in  time,  just  as  common  life  is  earlier 
than  Science.  But  in  both  there  are  now  innumerable 
shades  of  development  or  completeness.  It  may  be  safe 
to  say,  perhaps,  that  from  crude  concrete  perceptions  the 
first  predisposition  for  abstract  knowledge  arose,  and 
that  by  means  of  such  predisposition,  aided  by  language, 
or  signs,  the  first  crude  abstract  guesses  were  formed. 


76  FALLACIES.  [Part  L 

But  the  history  of  knowledge,  from  the  earliest  evidence 
attainable,  is  a  record  of  the  alternate  and  mutual  pro- 
duction, correction,  and  illumination,  of  one  kind  of 
judgment  by  the  other.  At  the  present  stage  of  pro- 
gress, as  will  be  seen  in  speaking  of  the  kinds  of  Proof, 
there  are  thus  in  operation  two  somewhat  conflicting 
methods  of  testing  truth, — two  methods  which,  though 
often  opposed  as  rivals,  and  either  of  which  may  at 
times  become  unimportant  or  inapplicable,  are  yet  to  a 
great  extent  capable  of  being  employed  in  one  and  the 
same  investigation.  Our  theories  require  to  be  grounded 
on  facts,  and  also  to  be  confronted  with  them:  but  to 
see  our  facts  in  the  light  of  theory,  though  a  dangerous 
habit,  is  in  some  ways  a  useful  one.  No  practical  mind 
can  desire  wholly  to  dispense  with  the  fonnulated  results 
of  all  past  observation.  Nor,  perhaps,  could  such  a 
desire  be  really  satisfied :  it  is  difficult  to  find  a  single 
case  of  observation  that  is  quite  free  from  the  influence 
of  our  general  knowledge.  Whatever  may  be  true  of 
the  earliest  concrete  assertions,  at  the  present  time 
every  concrete  assertion  put  'forward  as  a  thesis  carries 
with  it  a  remote  and  indirect  reference  to  numerous 
*  laws '  assumed.  By  implication  it  declares  the  posses- 
sion not  only  of  some  one  piece  of  abstract  knowledge 
but  of  many;  it  professes  the  knowledge  not  only  of 
a  law  but  of  conflicting  tendencies,  by  means  of  which 
the  special  circumstances  can  be  allowed  for  and  a  total ' 
balance  struck.  Thus  the  concrete  proposition  (when 
80  far  developed  as  to  become  a  thesis  for  proof)  is 


Chap.  HI.]  MAIN  KINDS  OF  THESIS.  77 

always  full  of  abstract  propositions  unexpressed.  Some- 
what as  the  trained  ear  can  detect  the  overtones  in  a 
musical  sound,  the  logical  mind  detects  the  hidden  as- 
sumptions in  a  concrete  proposition.  The  abstract  pro- 
position also  certainly  professes  an  acquaintance  with 
concrete  facts,  but  not  quite  in  the  same  manner  as  the 
concrete  proposition  professes  a  knowledge  of  the  laws  of 
Nature  as  bearing  on  the  special  circumstances  of  the 
case  under  consideration;  for  since  the  abstract  propo- 
sition expressly  avoids  saying  anything  about  special 
circumstances,  the  assertion  made  is  almost  infinitely 
simpler.  Practically,  of  course,  the  '  overtones '  in  a  con- 
crete proposition  are  mostly  overlooked,  but  it  is  their 
existence  that  constitutes  the  chief  weakness  of  un- 
aided common-sense.  What  seems  to  common  sense 
more  indisputable  than  that  this  given  action  is  a  case 
of  '  firmness '  or  '  strength  of  character,'  or  '  courage  ? ' 
Perhaps  a  deeper  insight  would  show  that  among  the 
special  circumstances  must  be  included  ignorance  of  con- 
flicting claims,  or  ignorance  of  danger. 

There  still  remains  to  be  noticed  that  very  common 
form  of  proposition  which,  when  two  concrete  things 
are  already  given  as  having  occurred  or  as  existing 
successively  or  simultaneously,  asserts  causal  connexion 
between  them.  When  we  say,  for  instance,  'Your 
hasty  speech  was  the  cause  of  all  the  disturbance,'  or, 
*  It  is  this  pillar  that  supports  the  building,'  is  the 
assertion  properly  abstract,  as  implying  some  law,  or 
concrete,  inasmuch  as  it  speaks  directly  and  expressly 


78  FALLACIES.  [Pabt  I. 

of  individual  facts  ?  Such  propositions,  I  hold,  may  be 
used  for  either  purpose,  or  for  both  together.  It  is  diffi- 
cult to  say  for  which  they  are  most  often  applied,  or 
even  which  is  most  often  their  primary  meaning.  On 
the  whole  one  would  perhaps  be  inclined  to  call  their 
concrete  meaning  primary,  and  to  say  that  the  abstract 
meaning  was  rather  insinuated,  or  implied,  than  directly 
intended  as  an  assertion.  But  in  practice  it  will  be 
found  that  these  assertions  are  largely  used  for  appa- 
rently confirming,  by  means  of  facts  experienced,  causal 
laws  already  more  than  half  believed.  And  since  the 
abstract  meaning  has  a  wider  importance,  and  since 
moreover  if  the  assertions  be  true  in  the  concrete  there 
must  also  be  some  true  abstract  assertion  behind  them, 
it  seems  best  to  view  them  as  capable  of  both  a  concrete 
and  an  abstract  meaning,  the  disproval  of  either  of  which 
would  disprove  both.  For  convenience,  then,  we  may 
speak  of  these  as  Abstract-Concrete  propositions,  if  it  be 
clearly  understood  that  they  form  no  new  distinction  in 
kinds  of  meaning,  nor  interfere  with  the  division  already 
made  (of  meanings,  not  of  forms  of  words)  into  abstract 
and  concrete. 

At  the  end  of  the  book  (Appendix  E)  will  be  found 
a  table  (I.)  of  the  divisions  thus  far  made. 

IV.  Succession  and  Co-existence. 

There  are  not  many  minor  distinctions  of  meaning 
in  propositions  that  call  for  notice  here.    We  are  not  in 


Chap.  III.]  MAIN  KINDS  OF  THESIS.  79 

search  of  all  the  varieties  that  can  possibly  be  distin- 
guished, nor  even  of  such  as  may  be  on  the  whole  the 
most  important  for  general  purposes,  but  only  of  such  as 
have  special  interest  for  the  purpose  of  discussing  the 
methods  and  the  dangers  of  Proof 

It  seems  necessary,  however,  to  mention  briefly  the 
distinction  between  propositions  asserting  succession 
(whether  backwards  or  forwards  in  time)  and  those 
asserting  co-existence;  or,  as  they  are  more  commonly 
called,  assertions  regarding  Causation,  or  Causal  sequence, 
and  assertions  which  merely  namne,  or  classify,  the  S,  or 
which  state  some  of  its  constant  concomitants  without 
necessarily  attempting  to  trace  them  to  a  parent  cause. 
Such  importance  as  the  distinction  has,  for  us,  flows 
from  the  fact  that  according  to  the  nature  of  the  asser- 
tion in  this  respect  is  to  some  extent  its  liability  to 
special  dangers. 

Wherever  indication  is  asserted,  whether  in  abstract 
or  in  concrete  propositions,  all  importance  turns,  of  course, 
on  the  degree  of  trustworthiness  of  the  sign :  *  some 
signs  being  more  certain  than  others,  but  even  a  vague 
symptom  being  better  than  none  at  all.  And  according 
as  the  assertion  points  backwards  or  forwards  in  time 
(S  a  sequent  of  ^,  as  in  'Valleys  — >  prior  denudation;' 
or  S  an  antecedent  of  ^,  as  in  '  Deficient  education  — > 
future  increase  of  crime ')  is  it  to  some  extent  open  to 

*  We  must  here  use  '  sign '  in  an  extended  meaning  also,  to  corre. 
spond  to  '  indication : '  so  as  to  say  that  in  every  proposition,  abstract 
or  concrete,  S  is  the  '  sign,'  and  &  the  thing  signified,  or  '  signification.' 


80  FALLACIES.  [Part  L 

special  and  different  dangers :  propositions  pointing 
backwards  being  liable  to  the  danger  of  overlooking 
'Plurality*  of  Causes;'  and  propositions  pointing  for- 
wards, to  that  of  overlooking  the  liability  of  one  cause 
to  be  counteracted  by  another. 

Thus,  to  take  first  Abstract  assertions :  it  is  seldom 
we  can  say  that  any  given  S  invariably  indicates  the 
past  existence  of  any  given  ^, — unless,  indeed,  the  ^ 
employed  be  so  vaguely  defined  as  to  be  of  very  little 
practical  service.  Every  event  (S)  we  may  no  doubt 
assert,  within  the  widest  empirical  limits,  indicates  the 
past  occurrence  of  soTne  other  event,  the  essential  part  of 
which  recurring,  S  will  recur :  true,  but  we  do  not  often 
find  this  doubted.  The  point  of  practical  importance  is, 
what  prior  events  does  S  indicate.  Or,  again,  every 
existing  human  being  has  certainly  had  (i.e.  indicates 
the  prior  existence  of)  a  human  grandfather :  this  also 
is  too  axiomatic  to  convey  practical  information,  though 
we  may  want  to  know  the  name  or  the  special  character- 
istics of  the  grandfather  in  question.  Almost,  but  not 
quite,  equally  rare  is  it  to  find  complete  invariability  of 
sequence  asserted,  except  thus  vaguely,  when  the  refer- 

•  Mr.  Carveth  Read's  term,  '  Vicarionsness  *  of  Causes,  though  less 
ambiguous,  I  only  do  not  use  because  the  name  '  Plurality '  appears  to 
be  so  firmly  established,  and  need  not  really  mislead.  The  reader  to 
whom  the  phrase  is  imfamiliar  must  notice  that  what  is  meant  is  the 
possibility  of  any  one  of  several  causes  having  produced  the  '  same ' 
effect,  as  where  '  one  kind '  of  death  may  be  due  to  heart-disease,  or  to 
a  fever,  or  to  yet  other  alternatives ;  the  name  has  nothing  to  do  with 
the  combination  of  causes,  as  where  a  death  is  due  to  mental  anxiety, 
plus  insufficient  food,  plus  an  illness  not  otherwise  necessarily  fatal. 


Chap.  HI.]  MAIN  KINDS  OF  THESIS.  81 

ence  is  forward  in  time.  A  shot  through  the  heart  or 
brain  is  perhaps  invariably  followed  by  death,  and  if 
there  were  interval  enough  between  the  two  events  we 
should  say  the  former  indicates  the  latter  as  sure  to 
happen:  but  favourable  seed-time  does  not  necessarily 
indicate  abundant  harvest,  since  in  the  interval  some 
unforeseen  counteraction  may  arise,  or  at  the  seed-time 
itself  along  with  certain  favourable  conditions  there 
may  have  been  an  unsuspected  enemy  sowing  tares.  So 
again,  we  may  often  predict  too  vaguely  to  be  of  much  real 
service.  Sunshine,  we  know,  for  instance,  always  follows 
rain,  and  may  be  expected  sooner  or  later ;  but  what  we 
most  want  to  know  is  when  to  hope  for  it,  or  under  what 
exact  conditions,  if  within  our  power  to  compass. 

Accordingly,  abstract  assertions  of  succession  are 
commonly  made  with  a  large  margin  for  the  incalculable. 
We  feel  fairly  contented  in  obtaining  any  hint  of '  law ' 
— any  knowledge,  that  is,  which  may  form  a  basis  for 
even  imperfectly  secure  inference  and  proof.  The  only 
alternative  to  '  Chance '  *  is  often  *  Tendency,'  and  in 
our  gladness  to  escape  from  Chance  we  dignify  this  as 
'Law.'  An  abstract  assertion  pointing  backwards  has, 
then,  to  deduct  from  the  trustworthiness  of  its  asserted 
indication  in  order  to  allow  for  the  possibility  of '  other 
causes  producing  the  same  effect ; '  and  this  even  where 

*  By  '  chance '  is  meant  in  this  connexion  no  more  than  the  con- 
tradictory  opposite  of  'known  law.'  Some  law  there  is  nowadays 
always  assumed  to  be,  but  that  the  conjunction  is  due  to  chance  means 
really  that  no  amount  of  limitation  of  S  or  of  ^  will  give  us  a  known 
law  between  the  two  things  so  designated.     See  also  Appendix  D. 


82  FALLACIES.  [Part  I. 

we  possess  a  real  *  Causal  Law.*  It  is  a  real  law,  for 
example,  that  prolonged  starvation  invariably  causes 
death.  But  stiU  we  are  very  far  from  being  able  to  say 
that  death,  wherever  found,  indicates  prolonged  starva- 
tion. And  in  like  manner  every  abstract  assertion 
pointing  forwards  in  time  has,  almost  in  proportion  to 
its  definiteness  and  consequent  practical  value,  to  allow 
for  possible  antidotes  or  counteraction. 

In  abstract  assertions  of  co-existence,  we  can  often 
attain  greater  certainty  of  indication  (for  practical  pur- 
poses, at  least,  and  within  narrow  fields),  but  even  here 
large  use  is  made  gratefully  of  incomplete  laws — indica- 
tions only  roughly  trustworthy,  true  only  on  unexpressed 
conditions.  We  may  know,  for  instance,  that  boys  '  as 
a  rule,'  delight  in  mischief,  and  we  may  make  real  use 
of  the  knowledge,  without  being  at  all  able  to  gene- 
ralise the  exceptions  so  as  to  state  a  quite  invariable 
law.  If  we  could  truly  say,  e.g.  '  All  boys  except  those 
who  are  physically  deformed  are  mischievous,'  our  indi- 
cation would  be  of  far  greater  value  than  while  we  can 
only  say  '  the  majority,'  or  '  many,'  or  '  the  average  boy,' 
or  any  other  vague  limitation. 

In  the  concrete  proposition,  on  the  other  hand  (except, 
as  will  be  presently  seen,  in  the  case  where  S  is  said  to 
deserve  the  navie  ^),  there  can  be  no  talk  of  the  asser- 
tion being  roughly  true.  The  given  S  was  either  as  a 
fact  preceded  by  ^  or  not ;  ^  either  wiU  or  wiU  not  be 
among  its  consequents  in  time.  Here,  accordingly,  it 
becomes  stiU  more  important  to  recognise  the  Plurality 


Chap.  III.]  MAIN  KINDS  OF  THESIS.  83 

of  Causes  and  their  liability  to  counteraction ;  and  hence 
the  purpose  of  distinguishing  the  two  kinds  of  assertion, 
namely  those  with  a  backward  and  those  with  a  forward 
reference, — assertions  explanatory  or  detective,  and  those 
which  predict.  As  regards  the  descriptive  or  classifying 
proposition  (where  S  is  said  to  deserve  the  name  §b) 
here  a  little  more  latitude  seems  inevitable.  Names  are 
altogether  so  loosely  applied — their  correct  meaning 
varies  habitually  within  such  wide  limits, — that  in 
giving  S  a  name  not  already  assumed  to  belong  to  it  of 
right,  we  may  well  be  content,  in  many  cases,  to  come 
somewhere  near  the  mark.  Is  this  man  civilized,  intel- 
ligent, learned,  unsteady,  idle,  brave  ?  Even  when  we 
judge  his  character  accurately  in  fact,  very  many  of  such 
questions  might  admit  of  the  double  answer.  Yes  and  No.* 

As,  then,  in  the  case  of  explanatory  or  detective  pro- 
positions the  main  difficulty  flows  from  the  Plurality  of 
Causes,  and  in  predictive  propositions  from  the  liability 
of  one  cause  to  be  '  counteracted '  by  others ;  so  in  pro- 
positions of  co-existence  the  danger  is  that  of  taking  for 
'essential'  something  that  is  'accidental'  merely, — i.e. 
of  believing  'always'  when  the  real  truth  is  'some- 
times.' For  if  the  proposition  be  concrete  (as,  'This 
man  is  a  fool ')  it  still  professes  abstract  knowledge, — 
knowledge  of  the  essential  qualities  which  go  to  form 
the  meaning  of  the  predicate  in  question. 

Tables  II.  and  III.,  in  Appendix  E,  show  concisely 
the  results  of  this  section. 

♦  See  also  pp.  124,  133,  184,  189,  vnf. 


CHAPTER  IV. 

THE  LAW  OF  COUNTER-INDICATION. 

As  the  presence  of  one  thing  may  indicate  the  presence 
of  another,  so  may  presence  indicate  absence,  or  absence 
indicate  presence,  or  absence  indicate  absence.  All  these 
are,  of  course,  equally  assertions  of  indication.  Thus 
a  negro's  coloured  skin  may  be  asserted  to  indicate  the 
presence  of  a  cheerful  temperament,  or  the  absence  of 
some  other  qualities ;  and  the  absence  of  pain,  in  certain 
cases,  to  indicate  the  presence  of  paralysis,  or  the  absence 
of  inflammation. 

On  any  view  of  Logic,  the  real  'pons  asinorurm  is 
the  group  of  facts  here  to  be  generalised  under  the  one 
'Law  of  Counter-indication,'*  This  law  may  be  said 
to  lie  directly  at  the  root  of  the  ordinary  doctrines  of 
conversion  and  contraposition,  and  also  to  contain  an 
explanation  of  the  whole  syllogistic  process.     Difficult 

*  Mr.  MacColl,  who  formulates  essentially  the  same  law,  adopts  for 
it  the  name  contraposition.  But  contraposition,  in  its  usual  meaning, 
seems  never  to  have  had  quite  so  wide  an  application,  and  therefore  I 
prefer  *  counter-indication '  as  less  likely  to  mislead.  Cf.  also  Prof. 
Croom  Eobertson's  remarks,  in  Mind,  No.  i.  p.  148. 


Chap.  iV.]       THE  LAW  OF  COUNTER-INDICATION.  85 

though  it  is  to  state  the  law  in  perspicuous  language,  and 
intricate  though  some  of  its  consequences  may  be,  the 
principle  itself  is  really  extremely  simple,  and,  once 
grasped,  can  hardly  be  forgotten  afterwards.  It  needs, 
however,  some  special  definition  in  order  to  overcome  in 
the  first  place  the  difficulties  of  statement. 

The  words  '  presence '  and  '  absence '  are  until  further 
explained,  hardly  general  enough  to  express  all  that  is 
intended,  and  are  only  chosen  because  no  other,  iaore 
comprehensive,  names  appear  to  be  available.  The  pre- 
sence or  the  existence  of  a  thing  or  quality,  the  happen- 
ing of  an  event,  the  truth  of  an  assertion,  stand  on  one 
side  of  the  opposition  intended,  as  contrasted  with  the 
absence  or  the  non-existence  of  a  thing  or  quality,  the 
non-happening  of  an  event,  the  untruth  of  an  assertion. 
And  for  brevity  and  our  own  convenience  merely,  I 
wish  to  extend  the  use  of  the  two  terms  chosen,  in 
order  to  cover  these  diverse  meanings.  Accordingly 
such  assertions  as  that  '  human  beings  — >  human 
parents,'  or  that  'the  existence  of  discontent  in  India 
— >  bad  government,'  or  that  'the  falling  of  a  stone 
— >  the  force  of  gravity,'  or,  'If  he  is  weU  he  will 


certainly  go,'  etc.,  are  all  cases  of  '  presence '  indicating 
'presence'  in  the  sense  intended.  And  so  with  the 
indication  of  absence  by  presence,  and  of  presence  or 
absence  by  absence.  The  two  words  are  not  to  be  under- 
stood as  strictly  limited  to  their  ordinary  sense,  but  as 
stretched  to  include  the  wider  meaning  postulated  as 
above  for  the  sake  of  simplifying  the  expression. 


86  FALLACIES.  [Part  I. 

Now,  since  we  mean  by  S  the  whole  of  that '  thing ' 
which  constitutes  the  sign  or  datum,  and  by  ^  the  whole 
of  that  which  the  sign  signifies,  it  is  clear  that  if  we 
employ  symbols  to  express  respectively  that  thing  the 
'presence  or  absence  of  which  may  indicate  ^,  and  that 
thing  the  presence  or  absence  of  which  may  be  indicated 
by  S,  we  cannot  use  S  and  ^  themselves  for  such  a 
purpose  without  incurring  misinterpretations.  Instead 
of  them  it  would  be  better,  where  necessary,  to  use  the 
corresponding  small  letters  s  and  S.  Thus,  if  the  presence 
of  a  steady  pulse  — >  absence  of  fever,  '  steady  pulse ' 
and  '  fever '  are  respectively  s  and  S, '  the  presence  of  a 
steady  pulse '  is  S,  and  *  the  absence  of  fever '  is  ^. 
Finally,  if  we  call  that  S  or  ^  which  expresses  the 
'presence'  of  s  or  S,  a  positive  one;  and  that  which 
expresses  their  '  absence '  a  negative  one ;  and  if  we  call 
their  positiveness  or  negativeness  their  quality  ;  and  the 
change  from  positive  to  negative,  or  from  negative  to 
positive,  a  change  of  quality ;  the  law  may  be  stated  as 
follows : — 

All  indication  of  ^hy  8  (affirmed  or  denied)  is  ex- 
pressible as  indication  of  S  hy  ^  (afftrmed  or  denied), 
if,  and  only  if,  the  quality  of  both  S  and  ^  be  changed. 

Let  us  trace  the  operation  of  this  lawy  first  symboli- 
cally and  afterwards  by  means  of  examples.  And  for 
the  symbolical  expression  let  S  and  §b  stand  for  the 
positive  forms,  and  non-S  and  non-^  for  the  negative 
ones.     Then  the  sole  equivalent  of 


Chap.  IV.]       THE  LAW  OF  COUNTER-INDICATION. 


87 


(1) 

s^.       ^ 

is 

non-^  — ^  non-S 

(c/.  contraposition  of  A)  .* 

(2) 

S  — ^  non-^ 

» 

^  — ^  non-S 

(c/.  simple  conversion  of  E).* 

(3) 

non-S  — ^         ^ 

>» 

non-5'  —>         S 

(cf.  exclusive  disjunction).* 

(4) 

non-S  — >  non-^ 

)» 

^-^      s 

(c/.  No.  1,  above). 

and  the  sole  equivalent  of 

(5) 

S4^         ^ 

is 

non-^-f->  non-S 

{cf.  contraposition  of  0).* 

(6) 

S  -|^  non.^ 

>» 

^-H>  non-S 

(cf.  simple  conversion  of  I).* 

(7) 

non-S  +^          ^ 

>> 

non-^)  -t^         S 

(cf.  No.  3,  above). 

(8) 

non-S  +^  non-J> 

» 

J>+>      s 

(cf.  No.  5,  above). 

But  examples  will  perhaps  show  the  process  more 
clearly.  Take  first  the  assertion  that  "every  corrupt 
tree  bringeth  forth  evil  fruit "  (i.e.  presence  of  corruption 
in  the  tree  — >  ditto  in  the  fruit) ;  then  the  equivalent 
form  of  this,  and  the  sole  indication  implied,  would  be 

*  absence  of  corruption  in  the  fruit  — >  absence  of  cor- 
ruption in  the  tree '  (i.e. '  if  the  fruit  is  sound,  the  tree 
is  sound ').  What  the  proposition  does  not  tell  us,  but 
what  may  perhaps  be  known  to  be  ti-ue  from  other 
sources,  is,  either  that  corruption  in  the  fruit  indicates 
corruption  in  the  tree  (i.e.  "  every  tree  that  bringeth 
forth    evil    fruit    is   corrupt"), — which    would    be  the 

*  simple  converse  '  of  the  original  proposition, — or  that 

*  These  names  refer  to  some  of  the  ordinary  technicalities  of  Logic. 
They  are  well  explained  in  all  the  text-books ;  e.g.  Bain's  Dedwtion,  pp. 
113-116, 122. 


88  FALLACIES.  [Past  L 

soundness  in  the  tree  indicates  soundness  in  the  fruit — 
which  would  be  the  'reciprocal.'  From  the  original 
proposition,  we  can  indeed  get  the  denial  of  any  such 
law,  as  that  corruption  in  the  fruit  indicates  soundness 
in  the  tree  (i.e.  '  Some  corrupt  fruit  is  the  offspring  of  a 
corrupt  tree ; '  the  '  converse  per  accidena ')  ;  but  this, 
being  a  denial,  is  not  itself  a  statement  of  indication :  the 
sole  indication  is  that  which  in  the  A  and  0  propositions 
is  usually  called  the  '  contrapositive,'  in  the  I  and  E 
propositions  the  'simple  converse,'  and  which  in  all 
propositions  is  here  called  the  counter-equivalent. 

Or  take  (2)  the  assertion  that  'no  quakers  are  dis- 
honest '  (quaker  tenets  — >  absence  of  dishonesty.)  Of 
this  the  formal  equivalent  would  be  that  dishonesty  — > 
absence  of  quaker  tenets  (*  No  thieves  are  quakers '). 
Here  will  at  once  be  recognised  the  ordinary  simple  con- 
verse of  E,  our  rule  differing,  in  fact,  from  such  conver- 
sion only  in  being  applicable  more  generally,  so  as  to 
include  all  grammatical  forms  of  proposition,  so  long  as 
they  express  the  indication  of  non-^.  Thus  from  the 
conditional  sentence,  'If  it  be  true  that  he  has  come, 
then  it  must  be  false  that  he  has  broken  his  leg;'  we 
get  by  counter-indication,  'If  it  be  true  that  he  has 
broken  his  leg,  then  it  must  be  false  that  he  has  arrived.' 
Again,  from  (3)  "  He  that  is  not  with  us  is  against  us  " 
(or  *  Everyone  is  either  with  us  or  against  us,'  or  'All 
except  our  party  are  unfriendly')  we  get  by  counter- 
indication  some  proposition  meaning  that  all  except  the 
plainly  hostile  are  on  our  side ;  and  if  the  proposition 


Chap.  IV.]       THE  LAW  OF  COUNTER-INDICATION.  89 

should  prove  untrue  in  one  of  its  aspects  it  must  be 
untrue  in  the  other  also.  This  form  of  proposition  de- 
serves more  attention  in  Logic  than  it  sometimes  obtains, 
and  we  shall  presently  (p.  92)  have  to  devote  a  few 
words  of  special  notice  to  it.  It  is  perhaps  more  liable 
to  misinterpretation  in  respect  of  its  legitimate  counter, 
than  any  of  the  other  forms.* 

The  importance  of  the  Law  of  Counter-indication  is 
far-reaching  in  Logic.  But  so  far  as  relates  to  the  in- 
terpretation merely  of  the  meaning  of  assertions  it  may 
be  shortly  stated.  A  certain  proportion  of  indications 
there  are — a  comparatively  small  proportion,  however — 
which  really  '  cut  both  ways,'  or,  as  it  is  technically 
called,  allow  of  the  ' reciprocal' f  assertion  also.     Thus, 

*  As  examples  of  the  remaining  forms  may  be  given :  from  (4)  '  with- 
out trouble  there  can  be  no  success,'  '  the  attainment  of  success  shows 
that  trouble  has  been  taken  : '  from  (5)  '  typhoid  fever  does  not  neces- 
sarily show  that  there  has  been  defective  drainage,'  '  proper  drainage  is 
no  complete  safeguard  against  typhoid  fever : '  from  (6)  "  the  presence 
of  the  attribute  'habitual  tendency  to  drunkenness'  does  not  neces- 
sarily  show  the  absence  of  (or '  is  compatible  with ')  a  fair  amount  of 
industry "  '  the  presence  of  a  fair  amount  of  industry  does  not  neces- 
sarily show  the  absence  of  a  tendency  to  drunkenness '  (or,  from  '  some 
habitual  drunkards  are  fairly  industrious  '  '  some  fairly  industrious  men 
are  habitual  drunkards  *) :  from  (7)  '  absence  of  the  power  of  discrimi. 
nation  does  not  necessarily  mean  presence  of  the  power  to  generalise,' 
'  absence  of  the  power  to  generalise  does  not  necessarily  indicate  pre- 
sence of  the  power  to  discriminate  :  *  from  (8)  '  illness  does  not  necessarily 
mean  weakness,'  '  strength  does  not  necessarily  mean  health.' 

t  The  name  '  reciprocal '  will  be  here  slightly  extended  beyond  the 
ordinary  usage,  and  employed  to  mean  not  only  what  Prof.  Bain  calls 
{Logic,  vol.  i.  p.  Ill)  the  "  material  obverse,"  but  also  the  illegitimate 
converse  of  any  indication  (affirmed  or  denied)  ;  i.e.  the  converse  formed 
without  changing  the  quality  of  S  and  5.    Thus,  both  ' non-S  — ^  non.^ ' 


90  FALLACIES.  [Pabt  L 

evil  fruit  does  perhaps,  as  a  fact,  indicate  an  evil  tree. 
So  again,  while  a  certain  label  on  a  bottle  shows  that  it 
came  from  a  certain  firm  (S  indicates  ^),  we  are  also 
often  told,  in  the  same  breath,  that  "  without  such  label, 
none  are  genuine  "  (non-S  indicates  non-^) ;  and  while 
equilateral  triangles  are  equiangular,  equiangular  triangles 
are  equilateral.  From  these  and  similar  occasional  cases 
a  certain  looseness  has  affected  our  application  of  all 
words  expressing  indication  (the  word  *  indication '  itself 
seems  to  me  least  ambiguous  ot  any)  through  which  its 
essential  one-sidedness  comes  into  frequent  danger  of 
being  forgotten.  The  law  of  counter-indication  helps 
to  remind  us  that  sign  and  signification  are  not  quite 
identicaL 

Here  should  be  noticed  further  a  fact  which  interferes 
largely  with  what  may  be  called  the  positive  utility  of 
the  law, — the  fact,  namely,  that  s  is  so  often  a  mark 
whose  presence  or  absence  is  much  easier  to  recognise 
than  that  of  S.  When  Darwin  finds,  for  example,  that 
white  cats,  with  blue  eyes,  are  always  deaf,  the  counter 
equivalent  (absence  of  deafness,  in  cats,  — >  non-white- 
ness of  fur  or  non-blueness  of  eyes)  is  hardly  likely  ever 
to  be  used  as  a  direct  indication.  If  we  want  to  discover 
the  colour  of  a  given  cat's  eyes,  we  should  probably  use 
our  own,  by  way  of  direct  observation,  rather  than 
employ  a  series  of  experiments  upon  the  cat's  power  of 

and  *  &  —^  S '  would  be  forms  of  the  '  reciprocal'  of  '  S  ->  &.'  See 
also  Wundt's  remarks  on  'one-sided'  and  'mutual'  dependence  in 
general;  Logik  (Erkenntnisslehre),  pp.  214,  245,  317,  etc. 


Chap.  IV.]        THE  LAW  OF  COUNTER-INDICATION.  91 

hearing.  And  so  in  many  other  cases.  The  chief  value 
of  the  law  is  rather  restrictive  than  inferential, — namely 
to  prevent  our  supposing  the  reciprocal  necessarily  true. 

Readiness  to  accept  the  reciprocal  as  equivalent,  is 
one  of  the  strongest  tendencies  in  uninstructed  human 
nature.  Recognising,  for  instance,  the  rough  truth  of  the 
law  that  stupid  people  are  conservative,  the  superficial 
reasoner  is  apt  to  overlook  the  difference  between  this 
assertion,  and  that  '  to  be  conservative  — >  stupidity ; ' 
assuming  that  success  in  examinations  is  a  good  indi- 
cation of  hard  work  and  high  talents,  common  sense 
supposes  that  this  assertion  really  means  that  failure  in 
examinations  is  a  good  indication  of  idleness  or  incom- 
petence ;  only  with  great  difficulty  can  the  illogical 
mind  be  made  to  see  that  other  causes  of  such  failure 
can  possibly  exist  besides  the  one  or  two  most  superficial 
or  striking ;  and  when  the  plurality  of  causes  is  at  last 
recognised  here,  it  seems  to  shake  some  people's  faith  in 
the  positive  indication  also.  Professor  Jevons,  speaking 
with  a  wide  knowledge  of  students'  capabilities,  tells 
precisely  the  same  tale.  "A  man,"  he  says,  "who  is 
very  ready  at  integration  begins  to  hesitate  and  flounder 
when  he  is  asked  such  a  simple  question  as  the  follow- 
ing: 'If  all  triangles  are  plane  figures,  what  informa- 
tion, if  any,  does  this  proposition  give  us  concerning 
things  which  are  not  triangles  V"  To  some  extent  also, 
and  chiefly  where  symbols  are  employed,  no  doubt 
the  error  flows  from  a  mere  thoughtless  inclination  for 
balance,  or  antithesis,  or  symmetry.     Those  who  are  just 


92  FALLACIES.  [Part  L 

beginning  the  study  of  Logic  are  perhaps  especially 
apt  to  be  slaves  to  this  inclination,  De  Morgan  notices 
(and  Jevons  endorses  the  opinion)  that  the  average 
beginner,  when  asked  what  follows  from  'Every  A  is 
B,'  invariably  and  promptly  answers,  'Every  B  is  A 
of  course.^  One  cannot  help  feeling  that  the  cause  is  in 
such  cases  probably  not  very  deep ;  the  schoolboy  who, 
being  told  that  the  three  sides  of  a  certain  triangle  were 
equal,  triumphantly  inferred  that  the  fourth  side  must  be 
equal  too,  hardly  supplies  a  better  instance  of  simple 
want  of  thought. 

Most  of  all,  perhaps,  in  interpreting  the  thoroughly 
'  disjunctive '  proposition  (where  absence  is  asserted  to 
indicate  presence),  this  spirit  of  superficiality  may  be 
seen  in  harmful  operation.  That  is  to  say,  a  disjunction 
is  relied  upon  as  exhaustive  while  it  is  thought  sufficient 
to  prove  the  mere  assertion  of  difference.  Thus  'Con- 
servative' and  'Liberal'  are  certainly  different,  but  it 
does  not  follow  that  they  are  the  only  two  alternatives. 
The  counter-equivalent  of '  non-S  — >  ^ '  is,  as  shown 
above,  'non-^  — >  S,'  but  what  is  thus  wrongly  taken 
as  equivalent  is  '  ^  — >  non-S,' — a  proposition  almost 
always  far  easier  to  prove. 

For  when  we  say  that  "  If  not  s,  then  S '  we  make  a 
large  assertion.  "We  divide,  in  fact,  the  whole  universe  into 
two  classes,  s  and  S,  and  boldly  assert  that  nothing  else 
but  these  exists, — that  whatever  is  not  in  the  one  class 
must  be  in  the  other.  Now,  to  do  this  with  s  and  not-s. 
or  with  %  and  not-S,  is  a  matter  of  common  occurrence ; 


Chap.  IV.]       THE  LAW  OF  COUNTER-INDICATION.  93 

SO  common,  in  fact,  that  whenever  we  use  a  general  name 
we  tacitly  accept  thus  much  responsibility.  But  in  such 
cases  the  only  difficulty  is  as  to  the  position  of  the 
dividing  line,  not  as  to  the  outer  limits  of  the  field  that 
may  lie  beyond  it :  '  not-s,'  or  '  not-S '  does  not  bind  us 
to  specify  otherwise  than  quite  vaguely  the  things  that 
lie  outside  our  defining  fortification. 

When,  however,  we  go  further  and  say, '  I  know  a 
positive  name  for  the  whole  class,  not-s  (e.g. '  not-con- 
servative '),  and  that  name  is  S,'  (e.g.  '  liberal ')  we  really 
profess  to  have  looked  out  from  the  citadel  s,  and  to 
have  scanned  the  universe  therefrom.  Of  course  there 
are  cases  where,  owing  to  special  circumstances  {e.g. 
artificial  limitation  of  the  '  universe,'  *  or  again,  the  case 
where  s  occupies  a  larger  extent  than  not-s)  this  is  prac- 
tically possible.  It  needs  little  courage  to  assert  that  all 
the  contents  of  my  pocket  are  either  letters  or  post- 
cards, or  that  if  a  man  does  not  believe  the  earth  is 
round,  he  must  be  slightly  crazy.  But  there  are  many 
more  cases  where  we  are  apt  mistakenly  to  suppose  the 
universe  scanned ;  and  this  danger  is  immensely  increased 
if  we  are  careless  enough  to  suppose  that  it  is  *  the  same 
thing*  (or  even  'practically'  the  same  thing)  to  prove 
the  reciprocal. 

*  De  Morgan  Mras,  I  believe,  the  first  to  observe  that  behind  most 
assertions  there  is  an  nnexpressed  limitation  of  the  range  of  their  extent. 
There  is  a  '  universe  of  Discourse '  beyond  which  the  assertion  is  not 
intended  to  apply.  *  Not- white,'  for  example,  is  predicable  solely  within 
the  universe  'colour;'  and  'Nonconformist'  excludes,  by  custom, 
heathens  and  atheists,  as  well  as  those  who  conform. 


94  FALLACIES.  [Part  I. 

But  mere  thoughtlessness  is,  no  doubt,  not  the  only 
explanation  of  the  tendency  in  question.  The  deepest 
source  of  it  seems  to  be  the  fact  that  provisional  belief  in 
the  reciprocity  of  indications  is  so  often  fruitful  as 
regards  the  earliest  guesses  at  unknown  truth;  for 
though  ^  (or  non-S)  may  not  exactly  indicate  S  (or 
non-^),  it  is  often  so  closely  connected  with  it  by  causa- 
tion that  in  finding  where  such  indication  fails  we  hit 
upon  the  real  law.  Corruption  in  the  fruit,  for  example, 
may  except  in  certain  assignable  cases  indicate  corruption 
in  the  tree.  Nevertheless,  in  Proof  as  distinct  from 
Discovery,  the  tendency  is  fatal,  and  needs  to  be  held 
in  severest  check.  It  is  unsafe  even  to  suppose,  as 
seems  so  natural,  that  mutual  indication  is  the  rule,  and 
one-sided  indication  the  exception.  Probably  the  pre- 
vailing attitude  among  the  illogical  is  best  expressed  as 
the  belief  that  any  law,  in  the  absence  of  proof  to  the 
contrary,  involves  a  '  fair  presumption,'  at  least,  that  the 
reciprocal  is  true;  while  fair  presumption  is  not  worth 
distinguishing  from  '  practical  certainty : '  the  real  fact 
being  that  the  most  an  abstract  indication  ever  involves 
is  a  fair  presumption  (and  that  not  always)  that  the  re- 
ciprocal is  worth  the  labour  of  investigation.  But  it 
seems  unnecessary  to  say  more  about  the  practical  value 
of  the  law  of  counter-indication :  it  merely  binds  up  into 
one  scheme  rules  whose  utility  is  already  well-known. 
This  is  the  case,  at  least,  as  regards  the  universal  affirma- 
tive and  the  particular  negative :  perhaps,  however,  the 
ease  with  which  the  disjunctive  proposition  is  liable  to 


Chap.  IV.]        THE  LAW  OF  COUNTER-INDICATION.   ^  95 

be  taken  for  the  mere  assertion  of  difference,  may  be  a 
less  familiar  fact. 

It  remains  to  ask  how  far  the  law  is  applicable  to 
concrete  propositions  The  answer  seems  to  be  that, 
though  formally  implied,  the  counter-equivalent  is  in 
concrete  propositions  never  directly  needed.  This  is  in 
fact  the  extreme  case  of  what  was  noticed  in  the  example 
of  the  blue-eyed  cats.  If  s  be  a  concrete  '  thing,'  we  have 
other  marks,  more  readily  applicable  than  non-^,  by 
which  to  prove  its  absence :  it  is  in  fact  known  to  us 
mainly  by  means  of  its  attendant  circumstances  as  a 
whole ;  and  %  is  only  one  of  these,  and  (by  hypothesis) 
not  the  most  familiar.  We  can,  indeed,  apply  counter- 
indication  to  concrete  matter  in  some  such  way  as  this : 
suppose  the  concrete  proposition  to  be  'This  murder 
— >  greed  of  gold ; '  if  we  are  certain  of  this,  and  also  of 
the  fact  that  in  a  given  prisoner's  case  the  greed  of  gold 
was  absent  (non-^),  we  no  doubt  may  infer  that  this 
murder  was  not  (non-S)  committed  by  him.  But  here, 
of  course,  it  is  not  '  this  murder '  whose  existence  we 
get  denied,  but  the  truth  of  the  theory  that  it  indicates 
the  prisoner  as  its  cause :  it  seems  that  the  result  is 
obtained  circuitously,  by  means  of  the  abstract  indi- 
cation involved, — namely  '  Any  one  who  committed  this 
murder  must  have  had  a  greed  of  gold,'  or  '  The  abstract 
possibility  of  this  murder  — >  such  motive,'  and  this 
motive  was  absent  in  the  case  before  us :  hence,  in 
the  case  before  us  '  this  murder '  was  absent  too.  This  is 
better  viewed  as  a  case  of  highly  elliptical  syllogism  than 
of  Immediate  Inference. 


96  FALLACIES.  [Part  L 

There  is  one  further  precaution  to  be  observed  in 
using  the  law ;  a  precaution,  however,  which  is  probably 
too  simple  to  require  notice  except  so  far  as  symbols  are 
employed.  And  perhaps  the  reader  already  recognises  * 
that  half  the  mental  confusion  that  exists  is  really  due  to 
the  use  of  symbols, — whether  such  symbols  are  imposed 
upon  us  by  the  real  need  for  abbreviation  (as  e.g.  in  the 
case  of  general  names),  or  by  what  may  appear  to  be 
the  wanton  pedantry  of  logicians.  It  is  easy  enough,  for 
instance,  to  see  that  the  proposition  'Every  man  is  an 
animal'  does  not  imply  that  every  animal  is  a  man, 
though  possibly  some  people  might  be  less  clear  about 
it  if  A  and  B  were  substituted  for  Man  and  Animal. 
Latet  dolus  in  generalihus.  But  here  the  source  of  con- 
fusion to  which  I  wish  to  draw  attention  is  that  due  to 
the  iime-element  in  indications.  Where  propositions  of 
co-existence  are  in  question,  no  difficulty  can  possibly 
arise,  but  in  the  case  of  succession  it  may  be  worth  while 
to  notice  that  where  S  indicates  (or  fails  to  indicate) 
future  §5,  non-^  indicates  (or  fails  to  indicate)  jpast  non- 
^,  and  where  S  indicates  (or  fails  to  indicate)  jpast  ^, 
non-§b  indicates  (or  fails  to  indicate)  future  non-^.  The 
examples,  given  above,  of  the  connexion  between  labour 
and  success,  or  between  typhoid  fever  and  the  drainage,! 
were  chosen  with  the  view  of  showing  this  necessity. 
Practically,  where  actual  examples  are  employed  the 
danger  is  not  likely  to  arise ;  but  in  the  absence  of  an 

•  With  Mr,  Keynes,  Mind,  No.  xv.  p.  366. 
t  See  note  on  p.  89  :  examples  (4)  and  (5), 


Chap.  IV.]        THE  LAW  OF  COUNTER-INDICATION.  97 

express  caution  there  might  perhaps  be  a  tendency  to 
suppose  that '  S  — >  future  ^ '  is  equivalent  to  '  non-^ 
— >  future  non-S,'  with  which  indication  (as  would  be 
seen  at  once  when  translated  into  full  language)  it  has 
really  nothing  to  do. 

Less  important  does  it  seem  to  mention  that  mere 
puns  form  no  exception  to  the  law.  No  reader,  I  hope, 
will  be  puzzled  by  the  fact,  for  example,  that  while  the 
presence  of  courage  clearly  indicates  *  presence  of  mind,' 
it  by  no  means  follows  that  '  absence  of  mind '  indicates 
anything  approaching  to  cowardice.  Logic  presents  ad- 
mirable opportunities  for  those  who  find  amusement  in 
punning, — a  fact  largely  recognised  some  two  thousand 
years  ago.  But  at  present  we  are  not  concerned  with 
any  difficulties  due  to  merely  verbal  quibbles. 

There  remains  little  more  to-  be  said  here  about  the 
subject-matter  of  Proof,  except  to  admit  as  unmistakably 
as  possible  that  the  view  of  propositions  here  taken,  and 
the  classification  here  made,  is  far  simpler  than  would 
be  required  for  almost  any  purpose  other  than  ours.  For 
Psychology  certainly,  and  also  for  the  doctrine  of  In- 
ference in  general  (as  contrasted  with  reflective  Inference, 
or  Proof)  very  much  more  would  be  needed.  But  in 
Proof  we  start  always  with  some  completed  Judgment, 
some  Judgment  developed  so  far  as  to  be  expressed, 
reflected  upon,  and  its  validity  called  in  question ;  hence 
the  growth  or  formation  of  the  Judgment  from  its  earliest 
traceable  stages  is  of  no  direct  concern  to  us.  Many  of 
the  varieties  of  grammatical  structure  correspond  roughly 


98  FALLACIES.  [Past  L 

to  shades  of  meaning  which  vary  both  in  definiteness  and 
strength  of  assertion,  and  in  richness  of  implication. 
These  are  in  themselves  of  high  importance :  but  before 
the  interest  in  these  arises  we  need  to  keep  perfectly 
clear  the  first  broad  distinction  between  proven  and  not- 
proven.  For  such  a  purpose  the  plan  which  commends 
itself  alike  to  common  sense  and  to  Logic,  is  that  of 
treating  the  proposition  as  something  put  before  us  in 
an  already  formed  condition;  put  forward,  that  is,  as 
conveying  intelligible  meaning  and  deserving  intelligent 
belief.  By  considering  it  a  pretender  to  these  qualities, 
and  then  proceeding  to  inquire  how  far  it  actually  falls 
short  of  attaining  them,  we  best  arrive  at  some  notion 
of  its  real  position  on  the  long  scale  between  worth  and 
worthlessness.  It  is  on  this  account  that  we  choose,  as 
being  of  directest  interest,  the  task  of  considering  in 
detail  the  series  of  possible  objections  that  can  be  brought 
against  any  thesis  set  up  as  worthy  of  belie£ 


CHAPTER  V. 
THE  PKOCESS  OP  PROOF,  IN  GENERAL. 

I.  The  Relation  between  Thesis  and  Reason. 

What  is  the  relation  between  a  thesis,  as  such,  and  any 
reason  given  for  it  ?  What  is  really  said  in  saying, '  the 
proposition  T  *  is  true,  because  the  proposition  R  *  is 
true '  ?  This  question  lies  at  the  root  of  the  doctrine  of 
logical  sequence. 

To  prove  an  assertion,  it  was  said  in  Chap.  I.,  is  to 
establish  it  in  full  view  of  hostile  criticism :  the  function 
of  the  advocate  being  to  find  and  bring  forward  reasons 
for  belief  or  disbelief,  and  the  function  of  the  judge 
being  to  weigh  the  evidence  brought  forward,  balancing 
the  arguments  for  and  against.  Our  concern,  it  has 
been  also  explained,  is  entirely  with  the  latter  of  these 
functions,  and  accordingly  we  may  dispense  with  all  con- 
sideration of  i\ie  finding  of  the  arguments. 

But  suppose  an  argument  already  found  and  pro- 
duced— suppose,  that  is,  not  only  a  thesis  brought  for- 

*  For  convenience,  T  and  E  will,  throughout,  be  occasionally  used 
for  '  Thesis '  and  '  Reason '  respectively. 


100  FALLACIES.  [Pabt  I. 

ward,  but  also  a  reason  or  reasons  in  support  of  it ;  *  by 
what  means  are  we  to  judge  of  the  binding  force  of  such 
argument,  how  test  the  validity  of  the  reasons  given,  or 
the  strength  of  the  evidence  adduced  ?  The  answer  to 
so  large  a  question  cannot  be  given  briefly  and  directly, 
except  in  words  too  general  to  render  real  assistance  in 
the  special  cases.  But  it  may  be  worth  while  first  to 
take  the  broad  and  distant  view.  Clearly  the  most 
preliminary  requisite  is  that  no  mistake  should  be  possible 
as  to  the  full  relation  between  Reason  and  Thesis,  as 
proposition  guaranteeing  and  proposition  guaranteed. 

We  elected  also  (p.  73)  to  neglect  the  distinction  be- 
tween categorical  and  hypothetical  propositions,  as  stand- 
ing outside  our  interest;  and  to  treat  all  propositions, 
whatever  their  grammatical  form,  as  alike  in  stating  a 
relation  between  two  terms.  But  in  order  to  do  this  it 
was  necessary  to  explain  that  the  terms  of  a  proposition, 
so  understood,  are  sometimes  themselves  propositions, — 
as  in  the  familiar  case  of  the  ordinary  hypothetical.  Now 
every  argument  may  be  viewed  as  a  proposition  of  this 
character,  with  subordinate  pronositions  as  its  terms. 
Every  argument  states  that  the  truth  of  E,  indicates  the 
truth  of  T.  Every  argument,  that  is  (to  apply  the  law 
of  counter-indication),  whatever  else  it  says,  makes  an 
assertion  expressible  in  the  formula : — 

K  -^  T,  aad 

non-T  — ^  non-B  : 

♦  Eeasons  for  any  thesis  are,  of  course,  reasons  against  the  opposite 
one ;  and  the  expression  may  therefore  be  safely  generalised  as  in  the 
text. 


Chap.  V.]   THE  PROCESS  OF  PROOF,  IN  GENERAL.     101 

whicli  is  the  symbolic  expression  for 

"  Grant  R,  and  T  follows,  and 
Deny  T  and  the  denial  of  R  follows." 

Or,  since  in  every  argument  the  truth  of  the  Reason  is 
asserted  to  guarantee  that  of  the  Thesis,  every  argument 
also  asserts  that  unless  the  Thesis  were  true,  the  Reason 
would  be  false. 

But  this  is  not  all  that  an  argument,  as  such,  asserts. 
There  is  another  element  in  every  case  of  attempted 
proof;  *  namely,  the  assertion  of  the  Tnaterial  truth  of 
the  Reason.  Without  this,  the  relation  asserted  would  of 
course  fail  in  relevance  to  the  matter  in  hand.  Unless 
the  reason  brought  forward  for  believing  a  thesis  be  itself 
asserted  to  be  true  in  fact,  the  argument  as  a  whole  would 
clearly  be  devoid  of  all  meaning.  It  is  no  argument  to 
say  that  if  some  false  or  doubtful  proposition  were  true, 
the  thesis  would  be  tnie:  to  support  (e.g.)  the  thesis 
"  England  is  on  the  verge  of  ruin  "  by  declaring  "  I  could 
appeal  to  statistics  if  only  they  were  different,"  or  even 
by  means  of  the  reason  "Because  possibly  statistics 
would  show,"  f    In  other  words,  failure  in  material  truth 

*  Cf.  Mr.  H.  MacColl.  Mind,  xvii.  55.  ♦'  The  statement  *  a,  there- 
fore I '  is  stronger  than  the  conditional  statement  *  a  implies  h,'  and 
implies  the  latter.  The  former  asserts  that  h  is  true  hecause  a  is  true  ; 
the  latter  asserts  that  h  is  true  provided  a  be  true." 

t  The  mere  mention  of  so  trivial  a  fact  as  this  second  element 
in  the  full  meaning  of  an  argument,  seems  to  need  some  apology; 
and  the  present  is  a  good  opportunity  for  remarking  that  wherever  self, 
evident  truths  are  enunciated  in  discussing  the  underlying  principles  of 
Logic,  the  purpose  is  by  no  means  to  convey  new  information,  but  rather 
to  go  through  the  duty — irksome  alike  to  reader  and  writer — of  formally 
6 


UNIVERSITY  OF  CALIFORNIA 
SAKTA  BARBARA  COLLEGE  UBRARX 


102  FALLACIES.  [Pabt  I. 

of  the  Reason  is  one  danger  which  every  argument  must 
avoid ;  the  sole  other  danger  being  that  of  failure  in  the 
fortrwl  adequacy  of  such  Reason, — i.e.  the  material  un- 
truth of  the  asserted  relation  between  R  and  T.  Any 
argument,  in  short,  is  liable  to  frustration  in  two 
ways : — 

(1.)  If  R  be  in  fact  untrue : 

(as,  perhaps,  where  England's  impending  bank- 
ruptcy is  appealed  to  in  proof  of  the  disastrous 
effects  of  Free  Trade.) 

(2.)  If  R  can  be  true  while  T  is  false  : 

(as  where  the  Sun's  movement  round  the  earth 
was  the  Thesis,  and  the  facts  of  'rising'  and 
*  setting '  were  the  Reason  given.) 

As  to  the  first  of  these  two  possible  attacks  on  Proof,  it 
is  clear  that  when  once  the  question  is  raised  whether  R 
be  true  or  not,  R  becomes  itself  a  new  Thesis,  and  must 
either  be  accepted  without  further  inquiry  or  submit  in 
turn  to  have  its  OAvn  grounds  produced  for  examination ; 
the  same  difficulty  recurring  until  a  basis  of  accepted 
truth  is  reached.  It  is  therefore  sufficient  for  Logic,  as 
such,  to  carry  the  analysis  of  the  methods  of  Proof  up  to 
the  point  where  the  formal  adequacy  of  the  reason  given 
is  secured,  thus  guarding  against  the  second  of  the  two 
attacks  :  for  the  first  of  them  leads  to  a  mere  repetition 
of  these  methods,  only  on  new  subject-matter.     Can  then 

registering  snch  facts,  merely  to  prevent  possible  misunderstandings,  and 
for  convenience  in  afterwards  referring  to  them. 


Chap.  V.]     THE  PROCESS  OF  PROOF,  IN  GENERAL.  103 

the  highly  generalised  statement,  given  above,  of  the 
nature  and  needs  of  formal  adequacy  be  translated  into  a 
shape  somewhat  more  convenient  for  application  to  actual 
arguments  ?  This  question  will  need  a  rather  circuitous 
answer. 

II.  Consistency. 

Probably  there  is  no  meaning  more  universally  asso- 
ciated with  the  epithet '  logical '  than  that  of  pushing  to 
the  extreme.  That  is  to  say,  a  man  is  popularly  said  to  be 
logical  (whether  as  a  term  of  admiration  or  of  the  reverse) 
in  proportion  as  he  shows  a  tendency  to  push  accepted 
principles  to  their  legitimate  outcome.  The  logical 
person  is,  as  a  rule,  uneasy  under  any  system  which, 
while  refusing  expressly  to  modify  inconsistent  principles, 
tosses  them  together  and  takes  the  mean  result.  In  his 
simplicity  he  supposes  that  whatever  is  asserted  as  true 
must  be  intended  as  strictly  true, — true  even  in  its 
extreme  case :  a  principle  false  in  a  single  instance 
becomes  to  him  fallible  altogether.  Hence  he  is  apt  to 
lack  that  quality  which  may  be  flatteringly  called  the 
delicate  tact  and  skill  required  for  handling  political  or 
ethical  fictions  with  advantage,  or  for  utilising  to  the  full 
certain  ancient  structures  thickly  coated  over  with 
anomaly.  The  English  Constitution,  English  Law,  the 
English  Church,  present  to  such  a  person  continual  diffi- 
culties. He  demands  a  clear  understanding  or  no  pretence 
of  it,  codification  or  else  anarchy,  absolute  submission  to 
authority  or  else  absolute  freedom  from  it.     In  this  sense 


104  FALLACIES.  [Part  I. 

it  is  that  the  French  are  called  in  every  newspaper  a 
logical  nation,  while  the  English  (with  the  exception 
perhaps  of  a  portion  of  the  reforming  party)  have  in 
many  quarters  quite  an  opposite  reputation. 

But  this  is  not  all.  Besides  reading  the  remoter 
consequences  of  principles  which  are  ready-made,  the 
logical  person  is  apt  to  generalise  principles,  on  his  own 
account,  out  of  isolated  facts.  Besides  being  tenax 
propositi,  he  is  eager  for  justice  to  be  dealt.  Not  con- 
tent with  demanding  that  an  actually  asserted  principle 
(a  'universal'  or  'abstract'  assertion)  shall  be  true  in 
its  extreme  cases,  he  is  inevitably  inclined  to  take  even 
purely  concrete  or  individual  assertions  as  covertly 
asserting  a  principle, — any  disclaimers  on  the  part  of  the 
assertor  notwithstanding.  Thus,  if  the  '  logical '  Legis- 
lator finds  some  individual,  or  some  class,  in  possession  of 
a  certain  right  or  subject  to  a  certain  duty,  he  is  always 
under  strong  inclination  to  extend  such  right  or  duty  to 
analogous  cases :  if  householders  and  lodgers  in  a  borough 
have  a  vote,  he  is  apt  to  view  them  as  members  of  a 
wider  class  including  (at  least)  householders  and  lodgers 
elsewhere:  he  resists  a  Permissive  Bill  on  the  ground 
that  it  is  'illogical'  to  allow  the  sale  of  liquor  in  one 
district  while  prohibiting  it  in  another, — if  alchohol  is 
pernicious  at  all,  he  argues,  it  is  pernicious  everywhere ; 
or  if  the  ratepayers  are  to  have  this  prohibitory  power 
they  must '  logically '  be  allowed  the  like  power  in  other 
cases,  until  there  might  be  nothing  left  of  individual 
liberty.     So  again,  he  considers  it  indefensible  to  protect 


CiCiP.  v.]      THE  PROCESS  OF  PROOF,   IN  GENERAL.  105 

one  branch  of  industry  without  protecting  all.  In  a 
word,  behind  apparently  simple  individual  facts,  he  has 
a  keen  eye  for  possible  principles  involved. 

In  appealing  in  this  way  to  what  is  after  all  only  a 
loose  and  popular  meaning  of  the  word,  I  must  not  be 
understood  as  laying  more  stress  on  such  meaning  than  it 
deserves.  Popular  usage  is  often,  of  course,  as  misleading 
as  etymology,  when  the  purpose  is  to  find  the  most 
accurate  sense  of  a  term  at  the  present  day.  But  as 
already  explained,  such  purpose  lies  altogether  outside 
our  interests,  our  only  desire  at  present  being  to  gather 
in  from  any  source  available  the  broadest  preliminary 
notions.  And  while  the  loosest  custom  is  ever  the  most 
widely  spread,  the  widest  custom  has  the  best  chance  of 
indicating,  however  vaguely,  the  more  permanent  founda- 
tions of  meaning. 

The  two  correlative  *  logical '  tendencies  just  noticed 
have,  it  is  true,  only  a  remote  and  indirect  connexion 
with  the  needs  of  formal  adequacy ;  but  their  recognition 
may  serve  very  well  to  bring  us  a  stage  nearer  to  the 
actual  point.  If  to  be  logical  is,  mainly,  to  be  consistent, 
perhaps  a  glimpse  at  the  nature  of  consistency  will  afford 
a  closer  view  of  the  point  in  question. 

The  Maxims  *  of  Consistency  (also  often  caUed  the 
"Laws  of  Thought")  are  commonly  given  as  three  in 
number, — The  Laws  of  (1)  Identity, — A  is  A ;  (2)  Con- 
tradiction,— A  is  not  not-A;  and  (3)  Excluded  Middle, 
— ^A  is  either  B  or  not-B.     Whenever  we  use  a  name,  we 

*  Bain  :   Logic,  i.  Introd.  sect.  22. 


106  FALLACIES.  [Pabt  L 

use  by  implication  the  whole  meaning  belonging  to  that 
name,  both  (1)  positively,  and  (2)  negatively:  and  (3) 
every '  thing '  either  deserves  any  suggested  name  or  does 
not.  By  the  first  Law,  for  example,  'a  man's  a  man/ 
whatever  else  he  may  also  be.  And  by  the  second,  we 
must  take  care  that  our  defining-line  is  clearly  drawn. 
What  is  outside  A  must  not  be  confused  with  that 
which  is  within  the  range  of  its  meaning.  A  name  may 
be  qualified,  i.e.  may  have  other  (compatible)  meanings 
added  to  it,  as  when  we  speak  of '  a  strong  man,  armed ; ' 
but  incompatible  meanings  cannot  *  be  joined  to  it  with- 
out reducing  its  emplojrment  to  absurdity  by  taking 
away  the  meaning  already  given ;  so  long  as  two  contra- 
dictory meanings  are  supposed  to  remain  in  force,  each 
neutralises  the  other,  leaving  the  total  name  a  blank.  A 
straight  line  which  is  also,  in  the  same  plane,  a  curved 
line,  is  no  line  imaginable  by  us  at  alL 

Trivial  though  these  twof  Laws  may  appear  when 
viewed  either  as  Postulates  of  Language  or  as  statements 
of  psychological  fact,  yet  as  practical  maxims  for  ensuring 
the  consistent  use  of  names  they  are  evaded  or  violated 
by  everybody  every  day;  and  though  it  may  well  be 
held  that  absolute  obedience  to  them  is,  in  the  present 
state  of  language  at  least,  practically  impossible,  it  cannot 
be  denied  that  as  ideals  they  have  a  certain  use.     At 

*  Except  as  hereafter  explained,  see  p.  139. 

t  The  third  law,  (excluded  middle),  deducible  from  the  other  two, 
first  comes  into  importance  when  we  deal  with  the  subject  of  misinter- 
pretation.    For  the  present  it  may  be  left  aside. 


Chap.  V.]  THE  PROCESS  OP  PROOF,  IN  GENERAL.     107 

present,  however,  our  sole  piirpose  is  to  connect  them  with 
the  needs  of  formal  adequacy  in  general. 

We  seem  to  have  made  perhaps  rather  an  abrupt  leap, 
fi'om  speaking  of  holding  to  Principles,  and  of  rational- 
ising our  isolated  beliefs  by  bringing  them  under  Prin- 
ciples, to  the  question  of  abiding  by  the  postulated 
meaning  of  names.  But  there  is  no  great  leap  after  all. 
A  general  name  may  be  viewed  either  as  something  to  be 
applied  (and  thus,  in  effect,  a  Principle)  or  as  something 
to  be  defined  (and  thus  to  be  brought  under  a  wider 
Generality).*  The  use  of  a  general  name  is  twofold 
always, — to  be  given  to  a  '  thing,'  and  to  signify  certain 
supposed  facts  about  that  thing.  Names,  in  fact,  so  far 
as  used  at  all,  can  only  be  used  as  terms  in  a  proposition, 
whether  as  S  or  ^  :  every  general  name  is  applicable  to 
something  namcable,  and  signifies  some  other  nameable 
thing  or  things.  'Man'  denotes  (as  Mill  phrased  it)  the 
individual  men,  and  connotes  the  attributes  essential  to 
the  class.  Accordingly  the  process  of  attempting  to 
abide  by  the  meaning  of  our  names  is,  at  bottom,  iden- 
tical with  that  of  attempting  to  abide  by  our  assertions : 
and  in  speaking  of  one  we  speak  of  the  other. 

Every  name,  then,  that  has  a  meaning,  by  virtue  of 
that  meaning  refers  the  object  named  to  its  place  in  a 
system  of  wider  and  narrower  classes :  to  state  the  full 
meaning  of  any  name  f  (or  as  it  is  technically  called,  to 

•  If  N  stand  for  '  general  name,'  then  we  may  symbolise  the  use  of 
names  as  S  — ^  N  — ^  S. 

t  Otherwise  than  by  merely  giving  a  synonymons  term. 


108  FALLACIES.  [Pabt  L 

define  the  corresponding  notion),  in  every  case  without 
exception  consists  in  mentioning  some  wider  class  {genus) 
of  which  the  things  designated  form  a  part,  and  also 
mentioning  the  marks  {difference)  by  which  the  part  in 
question  may  be  distinguished  from  the  whole  remainder 
of  the  wider  class.  Thus  '  city '  might  be  defined  as  '  a 
large  town  (genus)  possessing  a  cathedral'  {difference). 
And  if,  accepting  this  definition,  we  make  the  assertion 

*  Manchester  is  a  city,'  we  state  really  two  things  about 
Manchester, — (1)  that  it  is  a  large  town,  and  (2)  that  it 
possesses  a  cathedraL 

Either  of  these  two  elements  of  the  meaning  of  every 
significant  {i.e.  'general')  name, — the  generic  or  the 
differential  element — may  from  various  causes  become 
obscured  or  sink  out  of  sight.  One  set  of  minds  find 
a  standing  difficulty  in  seeing  the  wood  for  the  trees, 
another  set  habitually  fail  to  see  the  trees  for  the  wood : 
the  former,  fixing  their  attention  mainly  on  the  points  of 
difference,  forget  the  common  link  that  binds  the  members 
of  a  class  together;  while  the  latter  stop  at  the  broad 
resemblance,  disdaining,  or  dreading,  or  simply  not  per- 
ceiving, the  obscurer  difierences  of  detail.     The  term 

*  city '  of  course,  being  quoted  here  specially  on  account 
of  its  simplicity  of  meaning,  does  not  well  exemplify 
either  difficulty :  but  the  majority  of  general  names  do 
exemplify  it,  more  or  less.  A  negro,  for  instance,  is 
'man,'  with  a  difierence,  and  perhaps  the  disputed 
question  whether  he  is  a  '  man  and  a  brother '  will  supply 
an  example  of  what  is  here  meant — some  people,  through 


Chap.  V.]  THE  PROCESS  OF  PROOF,  IN  GENERAL.     109 

seeing  clearly  that  he  is  not  a  '  brother/  being  inclined 
to  treat  him  as  hardly  human ;  while  others,  through  the 
obvious  fact  of  his  humanity,  have  perhaps  rather  over- 
looked his  differential  qualities.  It  is  not  always,  then, 
so  simple  a  matter  as  it  might  seem  at  first,  to  take  care 
that  A  means  really  A,  and  not  at  all  not-A ;  and  what 
is  worse,  owing  to  the  unavoidable  faults  of  language  it 
is  only  possible  within  somewhat  naiTow  limits  to  "  call 
things  by  the  same  names  as  other  people."  But  here  it 
is  sufficient  to  notice  in  the  first  place  that  it  is  the  Law 
of  Identity  which  (viewed  as  a  practical  maxim)  bids  us 
recognise  the  generic  element  in  the  meaning  of  a  name, 
while  the  Law  of  Contradiction  draws  our  attention  to 
the  differential  line. 

Names,  then,  are  employed  in  Proof  as  tickets,  or 
marks,  or  signs.  Every  general  name  is  a  significant 
label,  intended  to  make  a  two-sided  assertion  about  the 
thing  that  bears  it.  And  consistency  demands  that 
whenever  we  apply  a  name  we  shall  be  prepared  to  face 
all  consequences  and  abide  by  the  full  meaning  of  such 
name :  to  fail  in  doing  so,  is  to  be  inconsistent,  and 
thereby  to  destroy  the  value  of  our  own  assertion. 

This  demand,  it  will  be  seen  at  once,  corresponds  to 
the  first  of  the  two  logical  tendencies  noted  above,  namely 
the  holding  to  our  Principles.  A  Principle,  in  the  sense 
there  used,  is  nothing  more  than  a  universal  or  abstract 
assertion.  To  bring  any  case  under  a  law  or  principle 
is  precisely  the  same  operation  as  to  bring  any  S  within 
the  range  of  a  name :  the  purpose  in  both  cases  being  to 


110  FALLACIES.  [Pabt  I, 

make  use  of  generalised  knowledge  already  supposed  to 
be  true.  On  the  other  hand  the  second  logical  tendency 
— extension  to  analogous  cases — is  a  much  more  com- 
plicated affair,  being  partly  mere  deductive  *  consistency 
and  partly  a  process  far  more  difficult  to  guard  from 
error.  The  main  feature  in  the  second  case  is  in  fact 
not  merely  the  application  of  abstract  assertions,  but  also 
their  formation, — a  process  which  has  often  to  be  carried 
on  with  dangerous  speed  and  without  the  aid  of  fully 
outspoken  statement.  Here  too,  however,  exactly  the 
same  two  fundamental  dangers  are  present, — namely  on 
the  one  hand  that  of  overlooking  points  of  difference 
(between  the  cases  supposed  to  be  analogous)  and  thus 
generalising  too  widely;  on  the  other  hand  that  of 
neglecting  points  of  resemblance,  and  thereby  not  ex- 
tending the  principle  far  enough.  In  both  kinds  of  Con- 
sistency (accepting  for  the  moment  the  popular  name)  all 
turns  upon  our  accurate  appreciation  of  the  points  of 
difference  and  resemblance :  but  in  Deductive  Consistency 
we  are  concerned  with  the  differences  and  resemblances 
generalised  and  acknowledged  already  in  the  names 
employed,  while  in  Analogical  Consistency  the  point  of 
primary  importance  is  the  nature  of  the  things  them- 

*  As  this  is  the  first  occasion  where  the  name  'deductive'  has  to 
be  here  employed,  it  may  be  well  to  explain,  for  those  to  whom  the 
term  is  unfamiliar,  that  deduction,  whether  used  in  Inference  or  in 
Proof,  is  always  the  process  of  interpreting  a  law  in  its  details,  or 
applying  it  to  the  particular  cases  which  it  is  intended  to  cover.  This 
may  be  easily  remembered  by  viewing  the  process  (Deduction)  as  a 
downward  one, — law  being  '  higher '  than  fact. 


Chap.  V.]  THE  PROCESS  OF  PROOF,  IN  GENERAL.     Ill 

selves,  and  the  extent  and  kind  of  difference  and  re- 
semblance really  existing  between  them. 

III.  Formal  Adequacy  in  general. 

By  failure  in  formal  adequacy  of  the  Reason,  is  meant, 
it  was  said,  every  case  where  R  can  be  true  while  T  is  false.  & 
It  now  becomes  important  to  look  more  closely  at  the 
nature  of  R  in  general,  inquiring  what  (if  anything)  is 
universally  characteristic  of  such  assertions  as  are  capable 
of  supporting  a  Thesis. 

Since  by  R  we  mean  only  the  reason  actually  given 
or  expressed,  it  must  be  admitted  that  there  is  no 
universal  property  of  R,  as  such,  except  those  already 
mentioned, — namely  such  as  are  involved  in  the  mere 
relation  between  any  Reason  and  any  Thesis.  But  if 
instead  of  the  *  Reason  given  *  merely,  we  speak  of  the 
whole  'rationalisation'  of  the  Thesis, — the  reason,  if 
any,  implied,  as  well  as  the  reason  expressed — the  case 
becomes  very  different.  For  two  elements,  express  or 
implied,  are  required  for  all  rationalisation:  (1)  a  Principle 
or  abstract  indication  (an  assertion  that  a  certain  sign  is 
trustworthy) ;  (2)  an  Application  of  such  Principle,  or  an 
assertion  that  the  sign  is  present  in  the  case  or  eases 
contemplated  by  the  T :  in  other  words,  all  rationalisa- 
tion may  be  represented  syllogisticaUy. 

Proof  is  thus,  in  an  important  sense,  the  counterpart 
of  Explanation.  The  two  go  hand  in  hand,  and  each  is 
only  possible  in  presence  of  the  other.    Just  as  explan- 


112  FALLACIES.  [Pabt  L 

ation  always  demands  a  reference  to  some  wider  Gener- 
ality than  that  which  is  to  be  explained,  so  Proof  always 
demands  a  reference  to  some  wider  Generality  than  that 
which  is  to  be  proved.  To  explain,  and  to  prove,  consist 
essentially  in  this.*  Both  are  forms  of  '  rationalisation.' 
It  must  not  indeed  be  supposed  that  such  *  wider  gener- 
ality' is  always  in  the  first  place  formulated,  even  in 
thought, — much  less  in  language.  The  kind  of  evidence 
called  circumstantial,  for  instance,  and  still  more  the 
argument  from  analogy  (or  'parallel  cases')  are  by  nature 
averse  from  any  such  restrictive  procedure,  preferring 
rather  to  keep  their  principles  as  dim  and  intangible  as 
possible.  But  none  the  less  is  some  principle,  however 
limited  (so  only  that  it  be  wider  than  the  thesis  itself), 
required  before  any  test  can  be  applied;  and  the  main 
business  of  Logic,  as  a  practical  science,  is  to  force,  in 
every  case,  such  principle  into  explicitness,  in  order  to 
see  whether  or  no  it  and  its  application  can  bear  the 
daylight,  or  stand  the  strain  of  stubborn  fact.  An 
argument,  like  a  chain,  must  of  course  be  tested  by  its 
weakest  part:  and  while  either  the  principle  or  its 
application,  or  both,  may  be  unwarranted  by  fact,  it  is 
the  principle  itself  which  presents  at  least  the  largest 
target  for  attack,  and  which  is  therefore  oftenest  the 
centre  of  logical  interest.  Behind  every  reasoned  belief 
there  is  at  least  one  abstract  proposition  more  or  less 

*  We  have  seen  above  (p.  108),  how  in  the  case  of  explaining  the 
meaning  of  a  name,  the  process  (Definition)  always  refers  the  thing 
named  to  some  higher  genua. 


Chap.  V.]  THE  PROCESS  OF  PROOF,  IN  GENERAL.     113 

vaguely  implied :  and  the  most  potent  engine  of  disproof, 
— and  through  disproof,  of  proof, — is  the  process  that 
brings  to  light  these  underlying  abstract  propositions,  in 
order  that  their  validity  may  be  called  in  question.  The 
rationalisation  of  knowledge  is  its  reference  to  principles 
sufficiently  secure  from  criticism ;  and  it  is  the  Syllogism 
which  helps  us  to  force  these  principles  into  explicitness 
in  any  given  case,  and  so  enables  us  to  inquire  into  the 
foundation  on  which  the  thesis  rests. 

In  all  complete  rationalisation  of  a  thesis,  then,  there 
is  always,  implicitly  at  least,  one  indication  used  as  an 
indication,  and  therefore  abstract.  This  we  shall  call  the 
Law  or  Principle.  And  there  is  also,  implicitly  at  least, 
a  claim  that  the  case  or  cases  spoken  of  in  the  thesis 
come  under  such  law.  Whether  this  (the  'minor 
premiss ')  be  itself  an  abstract  or  a  concrete  proposition, 
it  is  equally  called  the  Application.  The  doctrine  of 
the  Syllogism,  whatever  other  value  it  may  possess,  is 
mainly  useful,  as  regards  the  rationalisation  of  a  thesis, 
for  drawing  attention  to  any  links  that  may  be  missing 
from  the  chain  of  complete  demonstration.  The  present 
is  not  however  the  best  opportunity  for  discussing  the 
details  of  this  operation.  In  this  first  general  view  of 
Proof,  it  is  sufficient  to  register  the  assertion  (afterwards 
more  fully  justified ;  see  pp.  212,  300)  that  Syllogism,  so 
far  as  the  said  purpose  is  concerned,  is  perfectly  general 
in  its  operation, — applies  to  all  Proof  whatever,  and  is 
not,  as  the  beginner  is  apt  to  think  it,  an  engine  to  be 
used  in  '  Deductive  Inference '  merely. 


114  FALLACIES.  [Pabt  L 

As  regards  Proof,  then,  the  uses  of  the  Syllogism  are 
chiefly  two : — 

(1)  When  a  person  has  already  admitted  the  truth  of 
a  principle  and  its  application,  to  bind  him  down  to 
every  particle  of  assertion  thereby  made.  In  this  use 
(as  we  shall  see  later)  it  is  an  argumentum  ad  hominem. 

(2)  When  any  thesis,  with  its  reason,  is  put  forward, 
to  enable  us  to  supply  whatever  is  wanting  to  complete 
the  Demonstration.  We  thus  apply  our  knowledge  of 
the  syllogistic  needs,  either  in  order  to  determine  the 
general  law  under  which  the  special  case  in  question  is 
supposed  by  the  assertor  to  come,  and  from  which  the 
thesis  is  supposed  to  derive  its  cogency, — and  this  with 
the  intention  of  inquii'ing  into  the  truth  of  such  under- 
lying assumptions :  or  else  (where  no  principle  has  yet 
been  formulated)  in  order  to  force  the  assertor  to  see 
what  must  still  be  done  in  order  to  stop  all  gaps  in 
conclusive  reasoning.  The  mode  of  these  operations  will 
be  more  fully  developed  in  the  sequel 


PAKT  11. 

THE  POSSIBILITIES  OF  EBBOB. 


SECTION  I.— BEFOEE  PEOOF. 

CHAPTER  I. 

INTRODUCTORY. 

Having  thus  sketched  in  outline  the  main  facts 
regarding  Assertion  and  Proof  which  are  of  preliminary 
importance,  we  are  now  at  liberty  to  begin  to  trace  the 
actual  bearing  of  these  on  the  detection  of  Fallacy,  by 
examining  in  detail  the  openings  at  which  error  may 
creep  in. 

When  an  assertion  is  first  enunciated,  the  Possibility 
of  Error  is  at  its  maximum,  and  we  have  now  to  exhibit 
the  process  by  which,  step  by  step,  this  possibility  may 
be  reduced.  We  are  only  concerned,  of  course,  with  its 
reduction  to  the  lowest  minimum  attainable,  not  at  all 
with  the  question  how  nearly  the  goal  may  absolutely 
be  reached.  There  will  be  no  harm  therefore  in  con- 
ceding that  after  Logic  has  done  its  utmost,  human  falli- 
bility remains :  only  let  us  protest  against  the  view  that 
since  the  moon  is  out  of  reach  there  is  no  sense  in  trying 
to  cultivate  the  earth. 

It   must   be    remembered   further,  that   since    the 


118  FALLACIES.  [Pabt  IL 

detection,  rather  than  the  total  avoidance,  of  Fallacy 
is  the  chief  object  of  our  present  inquiry,  this  method  of 
diminishing  the  chances  of  error  is  only  intended  to  be 
used  for  making  sure  that  such  and  such  a  fallacy  is 
absent.  By  trying  which  of  the  series  of  possible  attacks 
a  given  assertion  or  argument  can  fairly  meet,  we  at  the 
same  time  discover  its  point  of  weakness.  If  it  should 
pass  our  whole  examination,  we  discover,  not  that  it  is 
absolutely  free  from  all  possibility  of  error,  but  merely 
that  such  possibility  must  be  of  the  more  remote  kind 
which  for  practical  purposes  we  are  accustomed  to  accept 
and  disregard. 

In  the  Introduction,  the  possible  objections  to  any 
assertion  were  broadly  divided  under  three  heads : — 

(1)  The  objection  to  its  reality  as  an  assertion,  its 
capacity  for  Proof  or  Disproof;  an  objection  which  seeks 
to  condemn  the  Thesis  as  such,  and  without  even  in- 
quiring what  its  grounds  may  be,  as  containing  a  mere 
empty  shell  of  assertion,  without  a  meaning : 

(2)  The  objection  that  the  Thesis  is  a  inure  assertion; 
standing  entirely  alone  and  without  even  attempted 
support ;  or  in  other  words  that  nothing  has  been  done 
to  remove  the  burden  of  proof:  and 

(3)  That  though  '  real '  reasons  are  brought  forward 
in  support  of  a  '  real '  assertion,  such  reasons  are  insuffi- 
cient ;  which  objection  is  commonly  condensed  into  the 
two  words,  Non  Sequitur. 

The  plan  here  followed  then  will  be  to  take  each  of 
these  objections  in  turn,  to  discuss  them  by  the  help  of 


Chap.  L]  INTRODUCTORY.  119 

examples,  and  also  to  connect  them  with  the  broad 
principles  of  Logic.  And  first  in  order  comes  the  charge 
of  Unreality. 

In  a  former  chapter*  unreal  propositions  were  divided 
under  three  heads : — 

(1)  Tautologous,  or  '  essential,'  or  '  identical '  proposi- 
tions, or  'Platitudes':  (Jf  already  enunciated  in  the 
meaning  of  S). 

(2)  Self-contradictory,  or  suicidal,  propositions:  (J 
already  contradicted  by  the  meaning  of  S). 

(3)  Thje  case  where  any  term  used  in  a  proposition  is, 
from  any  cause,  devoid  of  meaning. 

In  each  case,  then,  it  is  clear  that  the  meaning  of 
the  terms  employed  is  the  important  matter,  and  that  it 
is  only  so  far  as  such  meaning  is  wanting  in  clearness  of 
conception  that  this  particular  fallacy  can  occur.  Defini- 
tion of  the  terms  is  accordingly  the  direction  in  which 
to  look  both  for  means  of  detecting  the  fallacy  and  for 
safeguards  against  the  first  of  the  main  objections. 

•  See  pp.  43-48.  t  Symbol  first  employed  on  p.  51. 


CHAPTER  IL 
THE  KINDS  OF  UNREAL  ASSERTION. 

I.  Tautology,  or  Platitude.     . 

Taking  in  order  the  three  heads — Tautology,  Self-con- 
tradiction, and  Meaningless  Term, — it  may  be  of  service 
first  of  all  briefly  to  enlarge  the  explanation  above  given 
of  their  nature, — their  causes,  varieties  and  results. 

First,  then,  as  regards  Tautology.  Its  causes  and 
results  are  essentially  the  same  as  those  of  the  Fallacy 
known  as  Petitio  Frincipii,  or  begging  the  question. 
The  assertion  itself  revolves  smoothly  in  a  circle,  just  as, 
in  the  latter  case,  that  more  complex  kind  of  assertion 
known  as  an  '  argument '  may  be  seen  to  do.*  We  render 
the  assertion  unassailable,  by  simply  postulating  ab  initio 
(in  the  definition  of  its  terms)  that  it  shall  not  be  assailed. 
Psychologically,  indeed,  it  may  be  true  that  in  most  cases 
of  apparent  tautology  pure  and  simple,  there  is  really  a 
fluctuation  between  two  assertions  (closely  similar,  per- 
haps, in  form), — one  real  but  highly  insecure,  and  the 
other  verbal  and  thereby  safe  against  all  attack  on  the 

•  Cf.  tnyj-a,  p.  193/. 


Chap.  U.]       THE  KINDS  OF  UNREAL  ASSERTION.  121 

score  of  truth  ;  and  that  we  use  the  former  when  no  one 
is  looking,  the  latter  only  when  awkward  doubts  arise. 
Such,  perhaps,  would  be  a  fair  explanation  of  what 
George  Eliot  calls  "those  undeniable  general  proposi- 
tions which  are  usually  intended  to  convey  a  particular 
meaning  very  far  from  undeniable," — examples  of  which 
are  often  given  in  her  dialogues,  as  "  He  said  it  did  as 
much  harm  as  good,  to  give  a  too  familiar  aspect  to  re- 
ligious teaching ; "  or  "  The  coachman,  if  he  had  been 
asked,  would  have  said,  though  he  might  have  to  fall 
down  dead  the  next  minute,  that  property  didn't  always 
get  into  the  right  hands  ;"  or  "There's  no  knowing  what 
may  happen  before  Lady  Day."  But  such  cases  do  not, 
I  think,  account  for  the  whole  employment  of  these 
empty  forms :  and  where  the  assertion  is  purely  devoid 
of  all  forward  movement,  our  acceptance  of  it  as  bearing 
a  meaning  seems  to  be  due  to  essentially  the  same  slack- 
ness of  mental  tone  that  enables  us  to  draw  satisfaction 
out  of  circular  proof.  Strictly  speaking,  the  shifty 
assertions  above  noticed  belong  rather  to  Igiioratio 
Menchi, — a  subject  to  be  discussed  later:  the  fallacy 
being  in  such  cases  perhaps,  not  really  that  of  accepting 
as  capable  of  test  or  verification  a  proposition  which  con- 
tains no  real  subject-matter  for  Proof,  but  rather  that 
of  asserting  one  proposition,  and  believing,  or  trying  to 
establish,  another.  The  chief  motive  for  Tautology 
proper  seems  to  be  the  desire  to  say  something  (or  to 
accept  any  '  explanation '  rather  than  none)  on  a  subject 
of  which  our  knowledge  is  not  deep  or  exact.     Such 


122  FALLACIES.  [Part  IL 

desire  is  often  coupled  with  a  dim  feeling  that  caution  in 
expressing  ourselves  is  necessary :  as  in  a  passage  which 
may  be  quoted  from  a  certain  Tourist's  Guide — "The 
expense  of  travelling  on  the  continent  depends  more  or 
less  on  the  habits  and  means  of  the  traveller,  and  his 
mode  of  journeying ;  and  likewise  on  the  rate  of  charges 
made  in  the  various  countries."  So  much  as  this  might 
have  been  known  without  the  help  of  any  assertion  at 
all,  and  the  belief  that  it  really  tells  us  anything  is 
obviously  an  illusion. 

It  must  further  be  noticed  that  there  are  occasions 
when  a  sentence  which  as  it  stands  may  seem  to  be  the 
purest  tautology,  possesses  a  real  value  in  spite  of 
having,  on  its  own  account  simply,  no  capacity  for  Proof. 
With  these  we  have  already  made  acquaintance,  namely 
in  the  statement  of  Postulates,  whether  such  Postulates 
are  general  or  special, — '  Laws  of  Thought,'  or  definitions 
of  given  names.  When  we  state  the  proposition  *A 
is  A,'  or  when  we  say  "  A  city  is  a  large  town  possess- 
ing a  cathedral,"  it  is  certainly  true  that  in  both  cases 
the  J  is  already  contained,  to  say  the  least  of  it,  in  the 
meaning  of  the  S.  But  these  assertions,  when  so  inter- 
preted, are  not  theses  set  up  for  Proof  at  all  They  are 
merely  our  means  of  registering  fundamental  assumptions, 
whether  general  or  special ;  and  they  pretend  to  be  no 
more  than  this.  Or  rather,  if  in  any  case  they  do  pretend 
to  capacity  for  Proof,  then  their  real  S  or  J  becomes 
a  very  different  one  from  that  which  appears  on  the 
surface.     It  is  conceivable,  for  instance,  that  the  expres- 


Chap.  U.]        THE  KINDS  OF  UNREAL  ASSERTION.  123 

sion  '  A  is  A  *  might  be  used  to  convey  some  such  meaning 
as  "  One  fundamental  postulate  of  thought  is  that  the 
meaning  of  a  term  is  capable  of  fixation," — a  proposition 
certainly  not  merely  verbal :  or  again  "  A  city  is,  etc." 
might  be  used  to  mean  "the  ordinary  (or  the  best) 
meaning  of  'city'  is,  etc." — a  proposition  whose  proof 
or  disproof  might  indeed  be  difficult  but  is  by  no  means 
necessarily  out  of  question.  These  cases,  therefore,  do  not 
affect  the  rule  in  any  way,  and  are  only  worth  mention 
in  order  to  bring  into  greater  prominence  the  difference 
between  asserting  anything  as  woHhy  of  credence,  and 
merely  registering  a  Postulate  in  order  to  let  the  full 
extent  of  our  assumption  be  openly  known. 

As  to  the  forms  in  which  Tautology  occurs,  it  follows 
from  this  interpretation  of  its  nature  that  it  is  chiefly  to 
be  found  in  propositions  that  profess  to  be  in  some  way 
explanatory,  whether  explanatory  of  names  or  of  facts. 
Thus,  a  definition  may  be  circular,  as  where  each  of  two 
contradictories  (as  '  luxuries '  and  '  necessaries ')  is  defined 
solely  by  the  other,  without  reference  to  something 
known  independently  of  both.  Or  again,  we  may  pretend 
to  explain  the  effect  of  opium  by  saying  that  it  has  a 
'soporific  virtue.'  Or  again,  we  may  bravely  put  for- 
ward an  abstract  proposition  (a  'law'  or  'principle') 
which  on  inquiry  turns  out  to  need  no  bravery  at  aU : 
as,  for  example,  when  we  lay  down  the  law  that  "  we 
ought  not  to  do  evil  that  good  may  come  " — if,  as  is 
usual,  *  evil '  be  defined  as  equivalent  to  '  that  which  we 
ought  not  to  do.'    A  proposition  of  this  kind  is,  no  doubt, 


124  FALLACIES.  [Paet  IL 

secure  against  disproof,  but  only  in  the  same  way  as  a 
dumb  man  may  be  called  secure  against  speaking  falsely, 
or  as  a  suicide  may  be  called  secure  against  the  less 
voluntary  kinds  of  death. 

Passing  by  the  grosser  cases  of  Tautology,  however, 
which  have  been  sufficiently  illustrated  in  the  earlier 
chapter,*  the  chief  problem  for  practical  interest,  in  this 
danger  as  in  all,  is  as  to  the  borderland  between  what  is 
fallacious  and  what  is  valid:  the  drawing  of  the  line 
that  separates  tautology  from  real  assertion.  The  great 
difficulty  in  deciding  in  practice  whether  a  giving  assertion 
is  tautologous  or  not,  flows  of  course  from  the  fact  that, — 
outside  names  with  a  purely  technical  or  artificial  mean- 
ing, as  '  triangle,'  or  *  city,'  or  *  fee  simple,' — the  meaning 
of  a  word  is  never  completely  fixed,  but  is  subject  to 
fluctuations,  slow  or  rapid,  gradual  or  irregular.  If 
there  were  some  competent  authority  to  which  appeal 
could  be  made  in  all  cases,  the  fallacy  of  taking  mere 
platitude  for  real  assertion  could  no  doubt  be  pointed  out 
in  any  case  with  ease :  we  should  simply  turn  to  our 
dictionary  and  compare  the  meanings  there  given  of  the 
words  employed.  But  as  yet,  unfortunately,  no  such 
universal  authority  exists. 

In  the  first  place,  when  we  speak  at  all  of  'the' 
meaning  it  becomes  important  to  decide  which  meaning 
is  the  object  of  our  inquiry.  For  the  same  word  may  at 
the  same  time  possess  several  dififerent  kinds  of  meaning, 
to  say  nothing  of  the  different  shades  (or  amount)  of 
•  Part  I.  Chap.  11; 


Chap.  II.]        THE  KINDS  OF  UNREAL  ASSERTION.  125 

meaning  which  it  may  bear  to  each  individual  who 
employs  it.  We  may  distinguish,  for  instance,  as  possible 
objects  of  inquiry : — 

I.  The  meaning  that  the  word  does  bear, 
(a)  to  '  most  people ' — vaguely  estimated : 

(j3)  to  some  particular  person  or  class  of  persons, 

(1)  under  the  impression  that  it  is  the 
'  correct,'  or  the  only,  meaning : 

(2)  As  a  postulate ;  i.e.  as  a  special  meaning 
consciously  put  upon  it  as  such  by  the 
speaker : 

II.  The  meaning  that  the  word  ought  to  hear, 
(a)  for  convenience  in  classification,  etc. 

(/3)  on  historical,  etymological,  or  other  grounds. 
It  seems,  therefore,  not  quite  satisfactory  to  say  with 
Professor  Bain  *  that  "all  newly  discovered  properties  are 
real  predications  on  their  first  announcement,  although 
immediately  on  being  communicated  they  become  verbal." 
In  one  sense,  no  doubt,  this  is  perfectly  true ;  but  the 
expression  quoted  needs  to  be  interpreted  with  care.     If, 
e.g.  a  chemist  were  to  announce  that  some  hitherto  sup- 
posed  element  is  really  decomposable,  we  can  hardly 
suppose  that  by  the  fact  of  such  mere  announcement  all 
the  rest  of  the  world  is  at  once  prevented  from  investi- 
gating the  matter  :  that  the  assertion  has  become  a  mere 
truism,  that  to  doubt  it  is  henceforth  impossible  and  to 
test  its  material  truth  absurd.     So  much  may  no  doubt 
be  safely  said  as  this, — that  our  ignorance  or  forgetfulness 

•  Deductive  Logic,  p.  70. 

7 


126  FALLACIES.  [Pabt  H. 

of  the  truth  of  a  proposition,  and  hence  our  power  of 
viewing  it  as  questionable,  is  what  makes  it  real  to  lis. 
But  the  point  of  first  importance  to  notice  and  remember 
is,  that  as  a  rule  when  using  a  name  we  can  only  have 
before  us  quite  a  small  part  of  its  total  meaning,  and  that 
we  do  not  habitually  remember  even  all  we  can :  we  only 
remember,  or  only  keep  prominently  in  mind,  quite  a  few 
of  the  propositions,  regarding  the  S  in  question,  which 
we  *  firmly  believe '  to  be  true,  and  as  a  rule  those  last 
discovered  are  least  regarded  as  forming  part  of  the  mean- 
ing of  the  name.  Hence  we  may  repeat,  and  with  a  real 
meaning,  propositions  expressing  even  facts  discovered 
long  ago, — as  that  the  Earth  is  round,  or  that  sunrise  and 
sunset  are  due  to  its  revolution.  For  purposes  of  Proof 
the  important  distinction  lies  solely  between  assertions 
capable  of  denial  with  a  meaning,  and  those  which  to 
deny  would  contradict  the  postulated  meaning  of  the 
name  employed  as  S. 

In  our  sense,  then,  the  reality  or  verbality  of  a  pro- 
position is  not  determined  once  for  all  by  the  fact  asserted 
having  been  already  discovered,  or  even  being  already 
generally  known ;  but  varies  with  the  purpose  for  which 
such  proposition  is  now  in  the  given  case  employed :  i.e. 
it  depends  upon  the  prominence  of  the  already-known 
fact  in  our  minds  at  the  time  of  using  the  name  or  names 
forming  the  S  of  the  proposition.  So  far  as  the  fact,  if 
known,  is  remembered,  so  far  is  the  proposition  verbal, 
and  any  attempt  to  prove  it  involves  of  course  a  circle  in 
our  thoughts :  so  far  as  the  fact  is  hidden  from  memory 


Chap.  II.]        THE  KINDS  OF  UNREAL  ASSERTION.  127 

SO  far  there  is  real  matter  for  Proof.  If  rotundity  enters 
into  our  notion  of  the  Earth,  then  it  is  obviously  futile 
to  ask  whether  the  Earth  (so  understood)  is,  or  is  not, 
round.  But  that  many  people  find  no  difficulty  in  keep- 
ing the  attribute  of  rotundity  entirely  absent  from  their 
notion  of  the  Earth,  habitually  building  up  that  notion 
piecemeal  from  remembered  landscapes,  if  it  may  not  be 
inferred  a  prioH,  at  any  rate  may  be  surmised  from 
the  existence  of  the  numerous  pamphlets — long  post- 
Copemican — catalogued  in  De  Morgan's  Budget  of  Para- 
dooces.  And  accordingly  the  assertion  of  the  Earth's 
rotundity  is  capable  of  being  '  real.' 

How  then  does  Definition  help  in  deciding  whether  a 
given  proposition  is  or  is  not  tautologous  ?  If  no  absolute 
and  fixed  meaning  ever  exists  (except  in  the  case  of 
certain  technical  terms)  how  can  we  establish,  in  other 
cases,  any  general  test  of  tautology  ? 

The  most  we  can  really  do  is  to  bind  the  assertor 
down  to  a  special  definition  of  his  own ;  to  ask  for  the 
special  meaning  which  he  intends  to  keep  in  view.  The 
meaning  of  a  word  is  much  like  the  "  market  value  "  of 
an  article, — a  matter  to  be  settled  between  the  parties 
concerned.  We  can,  it  is  true,  satisfy  our  sense  of  justice, 
or  of  general  responsibility  to  our  neighbour,  by  accusing 
him  of  ignorance  of  the  ordinary  meaning  (or,  if  we  are 
very  self-confident,  of  the  best  meaning)  of  the  words  he 
uses :  but  such  an  accusation  is  a  totally  different  one  from 
that  with  which  we  are  here  alone  concerned.  It  affects, 
no  doubt,  our  opinion  of  the  speaker's  general  level  of 


128  FALLACIES.  [Part  IL 

common-sense  or  of  education,  but  not  at  all  the  question 
whether  or  no  the  assertion  as  made  and  intended  admits 
of  Proof  and  Disproof.  It  should  be  remarked,  more- 
over, that  there  is  often  considerable  difficulty,  even  in 
this  way,  in  obtaining  valuable  results.  People  do  not 
as  a  rule  enjoy  being  cross-examined, — or  only  in  the 
rare  cases  where  both  assertor  and  questioner  are  simply 
anxious  to  avoid  mistakes ;  where  the  claim  to  oracular 
dignity  on  the  one  side,  and  the  spirit  of  mischief  or 
obstruction  on  the  other,  are  wholly  wanting. 

For  besides  the  real  danger  of  platitude,  there  is  an 
opposite  danger  to  be  avoided,  namely  that  of  unduly 
and  vexatiously  stopping  an  argument  to  have  the  terms 
explained.  Without  wishing  exactly  to  defend  those 
who  made  Socrates  drink  poison,  one  still  cannot  help 
recognising  that  there  is  a  limit  beyond  which  the  laud- 
able desire  for  definiteness  loses  its  value  and  becomes  a 
hindrance  and  a  snare.  There  is  something  so  fatally 
easy  in  the  attitude  of  a  sceptic  or  mere  questioner. 
Any  child  can  keep  demanding  explanations,  any  man 
sufficiently  stubborn  can  delay  the  most  important  truth 
by  pretending  not  to  understand  its  import.  An  obstruc- 
tive policy  of  this  kind  requires  no  great  intellectual 
power,  and,  when  adopted  solely  for  obstructive  pur- 
poses it  demands,  as  much  as  anything,  a  rule  of  urgency. 
Life  is  not  long  enough  for  exhaustive  explanations. 

Here  at  the  outset,  then,  we  find  two  opposite  dangers, 
and  no  exact  rules  can  be  given  for  avoiding  either.  The 
most  that  practical  Logic  can  do  is  to  set  up  an  ideal  of 


CuAP.  II.]        THE  KINDS   OF  UNREAL  ASSERTION.  129 

clearness  and  precision,  and  to  demand  that  where  we 
fall  short  of  it  we  shall  show  fair  cause  for  doing  so, — e.g. 
the  need  for  saving  time  or  for  getting  work  accomplished. 
The  assertion  that  explanation  ought  in  a  given  case  to 
be  unnecessary  can  of  course  be  proved  like  any  other. 

II.  Self-Contradiction. 

Whereas  Tautology  is  chiefly  a  failing  of  feeble  or  timid 
folk,  self-contradiction  is  a  danger  to  which  the  rash  and 
immature  seem  specially  liable.  As  above  remarked, 
it  is  more  often  a  fault  in  expression  than  in  thought. 
Half  the  Irish  '  bulls '  (an  Irishman  once  explained  to  me) 
are  merely  expressions  that  are  too  epigrammatic  for 
the  slow-moving  Saxon  mind.  And  of  course,  where  this 
is  the  case,  such  assertions  can  always  be  translated  into 
sober  English  at  the  cost  of  a  little  trouble  or  prolixity. 
If  at  least,  in  any  case,  they  cannot  be  so  translated,  we 
have  obviously  no  other  means  of  getting  their  meaning 
clear  in  order  to  bring  them  to  the  test.  It  is  often  as 
painful  to  translate  an  epigram  as  to  explain  a  joke,  and 
a  good  example  of  such  translation  would  be  rather  hard 
to  find.  May  we  say  that  when  an  orator  once  declared 
that  his  party  had  "  a  majority  in  everything  except 
numbers,"  he  himself  was  fully  aware  of  the  verbal  con- 
tradiction, and  only  intended  smartly  to  rap  the  knuckles 
of  the  god  Majority  ?  The  answer  would  depend  upon 
our  knowledge  of  the  speaker's  mental  habits,  rather  than 
on  any  analysis  of  the  words  alone. 


130  FALLACIES.  [Pabt  II. 

But  paradoxers  (as  De  Morgan  called  them),  though 
sharing  with  some  great  discoverers  the  honour  of  being 
despised  at  first  by  Common  Sense,  do  not  always  re- 
semble pioneers  in  other  and  more  essential  points.  There 
can  be  no  doubt  that  a  good  deal  of  self-contradiction 
is  in  fact  rather  due  to  hastiness  or  crudity  of  thought 
than  to  any  nobler  origin.  As  Mr.  Herbert  Spencer 
notices,  "  the  ability  of  men  to  compromise  between  con- 
flicting beliefs  is  very  remarkable — remarkable,  at  least, 
if  we  suppose  them  to  put  their  conflicting  beliefs  side 
by  side ;  not  so  remarkable  if  we  recognise  the  fact  that 
they  do  not  put  them  side  by  side."  Mere  forgetfulness 
of  our  definitions  may  lead  us  into  inconsistency  just  as 
well  as  into  repetition :  the  main  difference  being  that 
whereas  one  element  among  the  causes  of  tautology  is 
often  the  sense  of  the  need  for  caution,  in  self-contra- 
diction this  sense  seems  to  be  wholly  wanting, — often  in 
fact  to  have  its  place  supplied  by  a  reckless  desire  for 
some  new  thing  at  any  price. 

Of  contradiction  between  S  and  J  (as  distinguished 
from  contradiction  within  a  term, — which  comes  mare 
properly  under  our  next  head)  it  may  be  said,  first, 
that  its  danger  depends  to  a  great  extent  upon  dilution. 
The  simpler  and  shorter  the  proposition,  the  less  easy 
is  it  to  find  really  dangerous  examples.  "  Twice  two 
are  five,"  for  instance,  runs  no  risk  of  being  mistakenly 
accepted  for  a  real  assertion ;  and  in  treating  the  subject 
for  our  purposes  we  may  in  the  first  place  cut  off 
from  consideration  the  cases  which  are  so  broad  and 


Chap.  11]        THE  KINDS   OF  UNREAL  ASSERTION.  131 

evident  as  to  amount  to  a  mere  jest.  Self-contradictions 
of  this  sort  are  endless,  from  the  heaviest  scholastic 
puzzle  to  the  latest  and  lightest  French  or  American 
comic  item ;  and  though  these  may  be  capable  of  pro- 
viding amusement,  they  are  not  likely  ever  to  lead  to 
serious  error.  It  follows,  however,  from  our  extended 
view  of  what  constitutes  a  proposition,  that  any  two 
(or  more)  separable  assertions,  if  intended  to  he  taken 
together,  may  be  viewed  as  one  whole  proposition ; 
and  that  therefore  we  may  have  a  case  of  unreality 
even  where  there  is  considerable  interval  between  the 
conflicting  assertions.  In  this  way  a  writer,  for  example, 
may  contradict  himself  plentifully  in  the  course  of  a 
book,  the  book  as  a  whole  attempting  to  pass  off  unreal 
assertions  upon  the  reader,  though  the  separate  items  of 
information  may  be  real  enough,  and  only  half  of  them 
false.  But  here  again  the  self-contradiction  is  com- 
paratively easy  to  detect.  A  more  difficult  and  subtle 
form  of  the  fallacy  arises  in  the  case  where  no  assertion 
is  expressly  made,  but  where  a  question  is  raised  and 
debated  as  if  an  alternative  answer  (yes  or  no)  were 
possible,  when  in  fact  one  of  these  answers  would  be  a 
tautology  and  the  other  consequently  a  contradiction. 
As  an  instance  of  this  may  be  quoted  the  question  '  Can 
one  individual  be  at  the  same  time  a  different  in- 
dividual ? ' — a  case  which  one  would  have  thought  too 
glaring  even  for  use  as  an  example,  if  it  had  not  been 
discussed  at  some  length  and  with  more  or  less  of 
genuine  perplexity  in  actual  writings. 


132  FALLACIES.  [Part  IL 

Here,  in  fact,  we  begin  to  get  a  glimpse  of  the  more 
serious  difficulties  in  detecting  and  avoiding  this  kind 
of  fallacy.  Speaking  broadly,  we  have  seen  that  self- 
contradiction  may  be  due  to  two,  almost  opposite,  causes, 
— mere  carelessness,  on  the  one  hand ;  and  on  the  other 
hand  all  that  may  be  included  under  the  name  'epigram,' 
a  scale  that  may  be  made  to  reach  all  the  way  from  simple 
impatient  condensation  of  a  sentence,  up  to  the  most 
praiseworthy  attempts  to  rise  above  the  artificial  barriers 
of  lanffuage.  Inconsistencies  of  this  latter  kind  cannot 
always  be  laid  to  the  account  of  light-brained  '  nihilism » 
of  thought,  but  are  rather  due  to  the  spirit  of  deep  in- 
quiry, casuistry,  or  over-carefulness.  And  the  form  in 
which  the  real  danger  oftenest  appears  is,  as  just  said, 
the  raising  debate  upon  unintelligible  questions. 

We  may,  then,  very  briefly  dismiss  from  consideration 
the  simpler  kind  of  self-contradiction,  since  here  there  is 
only  one  side  to  be  considered.  Every  one  will  probably 
admit  that  mere  carelessness,  or  confusion  of  mind,  is 
a  thing  to  be  on  the  whole  avoided,  and  only  requires 
to  be  pointed  out ;  which  may  as  a  rule  be  very  easily 
done.  Thus  when  Bishop  Butler,  in  his  'Analogy,'  re- 
marks that  where  there  is  the  slightest  prepoTiderance  of 
probability,  prudence  requires  us  to  act  accordingly,  and 
then  goes  on  to  say  that  in  questions  of  great  consequence 
we  have  to  be  content  with  probabilities  even  loiver  than 
this ;  it  is  not  hard  to  see  that  the  joint  assertion  is  of 
much  the  same  nature  as  the  saying  that  "  One  man  is 
as  good  as  another, — and  better."     So  too  when  a  writer 


Chap.  U.]        THE  KINDS  OF  UNREAL  ASSERTION.  133 

on  Ethics  laid  down  as  an  inducement  to  unselfish- 
ness the  rule  that  "the  less  we  think  about  being  re- 
warded, the  better  for  us,"  it  was  probably  a  mere  want 
of  consistent  thought  which  led  him  to  overlook  the  fact 
that  he  was  telling  us  in  the  same  breath  to  regard  and  not 
to  regard  consequences  to  ourselves.*  Such  slips  are 
however  of  very  frequent  occuirence,  especially  when  our 
case  is  weak. 

But  the  other  source  of  inconsistent  thought  con- 
stitutes a  standing  difficulty.  Nor  does  there  seem  to 
be  any  ultimate  and  quite  satisfactory  escape  from  it. 
It  depends  upon  the  real  uncertainty  of  the  line  between 
a  given  term  and  its  contradictory:  the  old  standing 
difficulty,  commonly  known  by  the  name  Sorites  (and 
more  anciently  called  Soros), — the  difficulty  of  getting 
a  truly  '  scientific  frontier '  for  the  names  we  use.  Where 
there  is  gradual  change  from  one  state  to  another,  or 
where  two  opposites,  however  unchanging,  may  be 
viewed  as  different  in  kind  only  through  being  widely 
different  in  degree,  how  are  we  to  fix  the  line  between  A. 
and  not-A?  Where,  for  example,  is  the  line  between 
'nation '  and '  tribe,'  between  '  solid  *  and  '  liquid,'  between 
'house' and 'cottage  ?'  Or  how  much  money  makes  a 
man  a  '  capitalist '  ? 

The  deeper  we  push  inquiry  into  the  exact  meaning 
of  any  given  name,  the  more  certain  it  becomes  that 
sooner  or  later  we  shall  find  ourselves  approaching  the 
main  quicksand  of  language, — the  fact  that  words  neces- 

*  Unless  indeed  it  was  merely  intended  as  an  argumentum  ad  hominem. 


134  FALLACIES.  [Part  IL 

sarily  postulate  definiteness  of  outline,  while  as  a  fact 
complete  definiteness  of  outline  does  not  exist  in  Nature. 
The  line  dividing  each  class  from  its  nearest  neighbour  is 
in  some  cases  {e.g.  between  infancy  and  full  age,  at  law) 
purely  and  confessedly  a  contrivance  of  our  own;  in 
other  cases  (as  between  '  good '  or  '  tall '  or  *  strong '  and 
their  contradictories)  purposely  left  vague  because  the 
phenomena  either  do  not  admit  of,  or  do  not  for  most 
purposes  require,  numerical  precision ;  in  other  cases  (as 
between  kinds,  and  even  varieties,  in  Nature)  is  pro- 
visionally useful  until  doubtful  instances  shall  arise.  But 
it  is  important  to  remember  (1)  that  in  all  cases  the  line 
is  so  far  an  artificial  one  that  it  is  we  who  have  made 
and  applied  the  names,  and  very  often  mistakenly,  for 
purposes  of  our  own;  (2)  that  in  all  cases  the  line 
professes  to  be  'length  without  breadth,'  while  as  a 
fact  there  always  remains  a  doubtful  margin,*  The  gap 
between  the  opposed  classes  is  infinitely  divisible,  is 
subject  to  constant  subdivision  as  time  goes  on,  and, 
though  it  is  being  gradually  narrowed  away  and  its  exact 
position  altered  by  the  acquisition  of  new  knowledge,  we 
can  never  know  that  the  furthest  subdivision  is  reached. 
A  notable  example  is  afforded  by  the  breaking  down 
of  ancient  barriers  that  is  even  now  taking  place  in 
all  departments  of  Natural  History  as  the  development 
theory  becomes  more  fully  understood :  one  of  the  best- 
known  problems,  for  example,  that  has  lately  risen  into 
high  importance,  being — If '  man '  has  directly  descended 

•  Cf.  Bain :  Logic,  bk.  iv.  chap.  i.  sect.  3. 


Chap.  H.]        THE  KINDS  OF  UNREAL  ASSERTION.  135 

from  '  beast/  at  what  point  in  the  history  of  such  descent 
does  man,  as  such,  emerge  ?  Various  accounts  have  been 
given  of  man's  differentia  from  other  animals;  among 
the  most  popularly  known  of  which,  perhaps,  are  that  he 
is  rational,  has  the  power  of  laughing,  the  use  of  language, 
or  of  tools,  or  the  practice  of  cooking  his  food.  So  far,  then, 
as  these  points  are  themselves  definite  and  clearly  under- 
stood, so  far  but  no  further  will  the  employment  of  any 
one  of  them  as  differentia  bring  clearness  into  our  notion 
of  'man,'  In  other  words,  we  may  (and,  for  the  purpose 
of  attaining  the  highest  possible  degree  of  accuracy,  must) 
push  inquiry  into  definitions  back  and  back  until  we 
reach  quite  firm  and  undisputed  ground.  Thus  it  may  be 
asked  what  constitutes  rationality  ?  Does  a  dog  reason, 
however  hastily,  when  having  once  been  scalded  he  ever 
afterwards  dreads  cold  water  ?  Is  a  sense  of  the  ludicrous 
absolutely  wanting  in  the  monkey,  and  always  present 
in  the  man?  What  is  language  but  vocal  sounds  con- 
veying a  meaning,  and  have  not  many  brutes  the  use  of 
these  ?  And  so  on.  One  definition  rests  upon  another, 
and  inherits  the  defects  as  well  as  the  virtues  of  its 
ancestry :  if  the  first  link  in  the  chain  is  faulty  all  the 
rest  must  sufier  to  that  extent.  Above  all,  the  dijfficulty 
shows  itself,  as  just  remarked,  in  that  the  further  back 
we  trace  man's  history  the  less  we  find  of  all  these  dis- 
tinctive qualities — the  more  imperfect  reason,  sense  of 
humour,  language,  tools  and  cookery :  and  the  inference 
becomes  to  many  people  irresistible,  that  at  a  still  earlier 
period  these  attributes  were  wholly  wanting,  or  if  present 


136  FALLACIES.  [Pabt  IL 

in  the  germ,  at  least  as  uncertainly  recognisable  as  they 
now  are  in  the  case  of  '  beasts.'  At  what  period,  then, 
precisely,  did  man  first  deserve  the  name  ?  If  it  be  ob- 
jected that  owing  to  the  scantiness  of  the  data,  man's 
remoter  history  is  merely  conjecture,  we  wiU  dispense 
with  this  instance  altogether,  and  instead  of  it  take  'man' 
defined  as  a  'grown-up  child:'  at  what  exact  period  can 
the  epithet  *  grown-up '  be  applied  to  him  ?  Most  of  us 
have  in  our  own  case  a  lively  remembrance  of  the  diffi- 
culties in  fixing  this  definition. 

It  is,  however,  not  our  purpose  here  to  attempt  to  do 
full  justice  to  the  difficulties  of  language,  or  to  do  more 
than  point  out  vaguely-where  some  of  them  lie.  Words 
and  their  meaning  are  altogether  full  of  unsuspected 
dangers,  but  to  treat  those  dangers  usefully  demands  a 
treatise  to  itself  When  we  consider  how  language  has 
grown,  thrown  up  at  first  by  savage  ancestors  living  from 
hand  to  mouth,  framed  to  meet  their  simple  needs  and 
to  express  the  results  of  their  desultory,  unassisted  obser- 
vation; altered  here  and  there  to  compromise  with  the 
growing  knowledge,  but  often  refusing  stolidly  to  admit 
past  errors,  and  merely  adapting  itself  by  some  circuitous 
fiction  to  the  new-fangled  notions  (as  'planet'  now 
means  no  longer  a  wandering  star  as  viewed  from  the 
Earth,  but  a  body  moving  round  a  sun — thus  including 
the  Earth  itself);  the  ignorance  of  one  age  taking  root 
and  hampering  the  effi)rts  of  the  next  to  see  things  more 
nearly  in  their  true  relations ;  always  in  fact  lagging  a 
little  behind   discovery,  and   delaying  the  birth  of  the 


Chap.  II.]        THE   KINDS   OF  UNREAL  ASSERTION.  137 

best  ideas  that  are  taking  shape  ;  when  we  consider  all 
this,  the  wonder  is,  not  that  confusion  frequently  occurs, 
but  that  any  consistent  expression  of  our  thoughts  is 
possible.  In  fact  it  is  probably  not  too  much  to  say  that 
we  can  never  be  quite  secure  from  all  taint  of  this  error. 
There  is  consolation,  however,  in  the  fact  that  a  good 
many  of  our  needs  too  are  rough  and  ready,  and  that  a 
good  deal  of  what  we  say  is  definite  enough  for  the 
ordinary  purposes  of  life.  Where  any  practical  harm  can 
be  traced  to  this  difficulty,  one  business  of  the  logician  is 
certainly  to  point  it  out ;  and  to  him  it  may  even  be  to 
some  extent  satisfactory  to  recognise  that  there  is  plenty 
of  work  to  do. 

In  the  case  of  self-contradiction,  as  in  that  of 
Tautology,  much  may  no  doubt  be  done  by  inquiring  as 
to  the  special  meaning  put  upon  S  by  the  speaker.  But 
the  artificial  character,  and  possible  unsatisfactory  results, 
of  this  safeguard  rise  here  into  greater  prominence,  since 
here  attention  is  attracted  rather  more  directly  and  openly 
to  the  defining  line  itself;  and  it  must  be  admitted  that, 
as  things  are,  it  is  often  unfair  (or  let  us  say,  unpractical 
and  obstructive)  to  press  for  exactness  of  line.  There  is 
some  value  even  in  vague  assertion, — at  least  where,  as 
often  happens,  nothing  better  can  be  obtained.  While 
allowing  that  until  the  contradiction  is  removed  by  some 
means.  Proof  or  Disproof  in  any  strict  sense  is  impossible, 
it  is  well  at  least  to  recognise  that  self-contradiction  is 
not  necessarily  so  flat  and  unprofitable  as  Tautology. 
Often,  of  course,  it  flows  from  mere  love  of  paradox,  often 


138  FALLACIES.  [Pabt  IL 

also  from  haste  or  inattention :  but  sometimes  it  will  be 
found  that  existing  language,  and  not  the  speaker,  is 
most  to  blame.  And  on  such  occasions  the  paradox  may 
usually,  with  sufficient  patience,  be  translated  into  a  real 
assertion ;  or  else  may  be  accepted  easily,  and  tasted,  in 
an  after-dinner  frame  of  mind. 

III.  Meaningless  Term. 

The  third  class  of  verbal  assertions  is  far  less  simple 
in  character  than  the  two  just  discussed.  To  treat  it 
fully,  in  fact,  we  should  have  to  exhaust  the  question  as 
to  the  limits  of  our  power  of  defining  effectively:  and 
this  can,  of  course,  not  be  attempted.  There  may, 
however,  be  some  use  in  showing  where  that  difficulty 
lies. 

But  in  the  first  place  any  term  may  be  meaningless 
either  (1)  simply, — i.e  through  want  of  definition;  or 
(2)  by  self-contradiction, — as  where,  in  a  complex  term, 
opposed  meanings  are  verbally  combined. 

This  second  case  is  so  closely  allied  to  the  kind  of 
verbal  assertions  discussed  in  the  preceding  section,  that 
not  much  remains  to  be  said.  The  difference  in  fact  is 
chiefly  a  grammatical  one ;  instead  of  saying  '  A  belongs 
to  the  class  not- A,  with  the  differentia  B '  {e.g.  '  man ' 
belongs  to  the  class  'not-man'  with  the  differentia 
'evolved'  or  'Life  is  a  gradual  death')  we  here  say  'A 
which  is  not-A  is  B '  {e.g.  '  Unconscious  hypocrites  are 
always  the  worst')  or  'B  is  A  which  is  not-A'  (e.g.  'A 


Chap.  II.]        THE  KINDS  OF  UNREAL  ASSERTION.  139 

continent  is  an  island  which,  through  mere  difference  of 
degree  in  size,  is  not  an  island ; '  which  assertions  might 
be  resolved  into  double,  or  joint,  propositions,  one  member 
of  which  contradicts  the  other.  But  there  is  some  use 
in  treating  these  self-conti-adictory  terms  separately, 
since  the  junction  of  incompatible  members  into  one  term 
has,  on  occasion,  certain  excuses  which  seem  to  apply 
more  specially  to  this  case  than  to  that  of  contradiction 
between  S  and  ^.  In  the  first  place,  when  a  term  has 
from  any  cause  lost  its  original  meaning,  there  is  of  course 
no  contradiction  in  combining  with  it  another  which 
contradicts  the  original  meaning  but  leaves  the  acquired 
one  free.  We  may,  for  example,  use  the  expression  '  bad 
goods,'  or  again  '  dry  humour,'  with  complete  reality  of 
meaning :  nor,  in  a  sentence  such  as  "  They  overlooked 
the  boundless  field  that  was  before  them  within  the 
legitimate  limits  of  the  Science,"  does  the  solecism  in- 
validate the  assertion  made.  Conversely,  too,  a  legitimate 
excuse  for  such  propositions  may  be  simply  the  desire  to 
call  attention  to  the  wrong  use  of  a  name,  as  in  'The 
present  Government  is  no  Government  at  all,'  or, '  If  your 
facts  are  false,  your  inference  is  useless.'  And  in  the 
second  place,  though  such  an  expression  as  a  'round 
square '  would  be  generally  ruled  out  of  court  as  meaning- 
less, it  seems  to  be  quite  allowable  to  speak  of  an  '  irre- 
gular square,'  or  of  '  a  globe  which  is  not  quite  globular. 
In  two  distinct  cases  under  this  head  there  is  a  recog- 
nised license  to  combine  terms  really  contradictory; — 
(a)  where  the  qualification  is  only  slight,  and  the  ex- 


140  FALLACIES.  [Pabt  II. 

pression  is  intended  to  be  merely  rough  and  ready, — as 
in  the  instances  just  given;  and  (b)  where  the  intention 
is  to  indicate  a  mean  between  opposed  notions,  as  in 
'Liberal-Conservative'  or  'blue-green  colour,'  or  'dead- 
alive.' 

Considerable  caution,  therefore,  should  be  exercised 
before  accusing  a  complex  term  of  being  really  suicidal : 
so  much  must  be  allowed.  But  when  all  possible  ex- 
cuses have  been  made,  there  remains  a  residuum  of 
cases  which  are  purely  fallacious,  and  which  are  by  no 
means  so  rare  as  might  be  supposed.  No  doubt  it  is 
chiefly  through  our  power  of  fluctuating  unconsciously 
between  two  different  beliefs  that  these  '  beliefs '  justify 
themselves  to  the  believer:  each  separately  is  seen  to 
convey  a  real  meaning,  and  it  seems  to  be  dimly  supposed 
that  since  each  is  a  positive  belief  (how  many  errors 
that  word  '  positive '  has  to  answer  for !)  the  total  result 
cannot  in  the  nature  of  things  be  a  non-entity.  Indeed, 
this  defence  has  been  sometimes  almost  openly  put  for- 
ward. No  doubt  where  the  sole  object  is  to  find  some 
form  of  words  '  true '  which  is  at  the  same  time  admitted 
to  be  '  incomprehensible '  we  have  a  contradiction  already 
as  a  starting-point,  and  it  is  perhaps  only  natural  that 
others  should  be  needed  to  support  it:  but  natural  or 
not,  such  a  process  is  apt  to  confuse  people's  minds  as  to 
what  is  meant  by  belief  at  all,  and  to  blunt  the  edge 
of  their  conscience  towards  themselves.  Possibly  this 
is  one  reason  why  the  habit  of  delighting  in  mysteries 
retains  its  hold  so  long. 


Chap,  n.]        THE  KINDS  OF   UNREAL  ASSERTION.  141 

Turning  now  to  the  case  where  a  term  lacks  mean- 
ing for  want  of  being  defined,  we  may  distinguish  in  the 
first  place  the  two  varieties  : — (a)  where  the  term  simply 
has  not  yet  been  defined  by  the  speaker ;  and  (6)  where 
a  definition  has  been  given,  indeed,  but  one  which  does 
not  really  explain. 

The  remedy  in  the  first  of  these  cases  is  of  course 
simple  enough ;  in  fact,  it  only  needs  mention  by  way  of 
introduction  to  the  second  case.  It  is  clear  that  when  we 
say  'x  is  good,'  or  '  every  man  is  x,'  there  is  no  subject- 
matter  for  proof  until  the  meaning  of  the  x  is  declared : 
and  that  if  it  can  be  declared  this  had  better  be  done  as 
soon  as  possible. 

What  then  are  the  limits  to  our  power  of  giving  names 
a  *  meaning '  ?  And  how  can  we  avoid  false  security  in 
the  matter  ? 

Since  for  definition  it  is  necessary  to  refer  to  some 
higher  class  (Genus),  it  is  clear  in  the  first  place  that  the 
most  general  notion  of  all — whatever  that  may  be — 
cannot  in  strictness  be  defined.  A  summum  genus, 
indeed,  is  usually  taken  to  mean  something  much  less 
extended  than  the  one  highest  genus  of  all,  namely  to 
mean  the  highest  in  any  given  series, — which  series  may 
of  course  be  a-  quite  arbitrary  selection  of  our  own.  Thus 
in  the  series  'Mineral,  rock,  stratified  rock,  limestone,' 
'mineral'  would  be  the  summum  genus,  although  a  higher 
class,  namely  'material  substance,'  might  easily  be  added 
to  the  series,  and  beyond  that  again  the  class  '  nameable 
thing.'     It  is  therefore  incorrect  to  say  that  no  summv/m 


142  FALLACIES.  [Part  IL 

genus  is  definable, — ^unless  we  are  speaking  only  of  the 
one  highest  of  all ;  or  unless  we  consider  the  inexplicable 
nature  of  this  ultimate  notion  to  vitiate  all  other  general 
names,  since  all  may  be  traced  up  to  it.  In  absolute 
strictness  there  seems,  in  fact,  to  be  no  escape  from  this 
difiiculty.  It  is,  no  doubt,  always  theoretically  lawful, 
though  not  always  practically  expedient,  to  push  inquiry 
into  the  meaning  of  a  name  back  into  Metaphysics, — just 
as  it  is  possible  to  demand  any  other  kind  of  ultimate 
explanation.  Any  objection  to  such  inquiry  can  only 
rest  on  the  plea  of  practical  needs ;  and  it  is  not  easy 
to  say  how  far  such  plea  itself  will  bear  stretching, — for 
who  is  to  decide  that  our  view  of  practical  needs  is 
sufficiently  long-sighted  ? 

It  certainly  seems  as  if — to  quote  Prof  Bain  * — "  the 
highest  universe  of  all  must  contain  at  least  two  things, 
mutually  explaining,"  and  that  our  highest  definitions 
must  accordingly  be  merely  circular.  Short  of  this 
ultimate  circle,  or  assumption,  however,  we  can  of  couree 
take  care  to  avoid  all  narrower  circles  in  defining. 

The  only  other  kind  of  delusive  definition  that  need 
be  noticed  in  this  connexion  is  that  sometimes  called 
'defining  ignotum  per  ignotius,'  as  where  a  writer 
explains  the  meaning  of  '  miracle '  to  be  "  an  abnormal 
exercise  of  constitutional  sovereignty  on  the  part  of  the 
very  divine  Ego,  in  respect  of  the  subsistere  of  the  cos- 
mical  selfhood  of  the  metamorphosed  Non-Ego."  Here 
we  can  of  course  either  take  the  requisite  pains  to  make, 

*  Deductive  Logic,  p.  59. 


Chap.  II.]        THE  KINDS  OF   UNREAL  ASSERTION.  143 

out  the  real  meaning  intended,  or  we  can  wait  for  some 
more  easily  intelligible  information.  But  until  such 
additional  process  has  been  performed,  any  proposition 
containing  '  miracle  '  as  S  or  J^  remains  obscure. 

As  regards  the  whole  question  of  the  need  of  definition, 
it  should  be  remarked  that  the  mere  fact  that  the  terms 
have  not  yet  been  defined,  or  have  been  imperfectly 
defined,  does  not  of  itself  necessarily  deprive  an  assertion 
of  all  '  real '  meaning.  If  this  were  so,  indeed,  the  con- 
veying of  information  would  be  even  a  more  lengthy  and 
troublesome  process  than  at  present.  It  is  only  when 
the  need  is  felt,  as  such,  by  the  person  addressed,  that 
the  assertion  can  fail,  in  this  way,  on  the  ground  of 
unreality :  for  where  the  audience  put  a  wrong  meaning 
(i.e.  one  not  intended  by  the  speaker)  on  the  terms 
employed,  there  is  misunderstanding,  perhaps,  and  there 
may  be  fallacy  on  one  side  or  the  other ;  but  inasmuch 
as  the  audience  do  put  some  meaning  on  the  assertion, 
it  is  real  to  them. 

IV.  Unreal  Assertion:  Concluded. 

We  have  seen,  then,  that  against  the  fallacy  of  taking 
an  unreal  proposition  for  a  real  one,  the  remedy  in  all 
cases  is  to  be  found  in  definition  of  the  terms  employed ; 
and  that  everything  depends  upon  the  special  meanino- 
given  to  them  by  the  assertor;  since  any  apparent 
tautology  or  cpntradiction  may  have  its  fallacious 
character  removed,  any  unknown  meaning  may  be  made 


144)  FALLACIES.  [Pabt  IL 

known  (within  the  limits  indicated  above)  by  such 
special  explanation.  We  have  seen,  too,  that  Tautology 
is  intimately  connected  with  the  fallacy  of  Petitio  Prin- 
dpii,  or  circular  proof,  while  self-contradiction,  except 
when  merely  used  to  condense  a  real  proposition,  is  really 
a  case  of  inconsistency, — sometimes  due  to  mere  careless- 
ness, sometimes  to  the  fact  that  lines  of  distinction  in 
nature,  on  the  preservation  of  which  all  consistency 
depends,  are  artificial  contrivances  of  our  own,  which  do 
not  exactly  fit  the  facts,  but  can  only  be  roughly  justified. 
And  as  regards  explanation  of  the  meaning  of  a  term,  we 
must  admit,  I  think,  that  there  is  a  point  beyond  which 
any  attempted  explanation  becomes  unreal ;  and,  hence, 
that  the  distinction  between  reality  of  meaning  and  mere 
verbality  has  a  value  only  so  long  as  we  keep  away  from 
the  deepest  difficulties. 

Before  leaving  the  subject,  there  are  one  or  two 
points  to  be  noticed  as  regards  unreal  assertion  in 
general  rather  than  any  special  form  of  it.  First  of  all 
it  may  be  well  to  distinguish  clearly  between  verbal 
assertion  {i.e.  tautology)  and  verbal  questions, — as  where 
a  disputed  point  is  said  to  be  "merely  a  question  of 
names."  Whately  has  expressed  as  concisely  as  any  one 
the  distinction  between  verbal  and  real  questions, — "If 
it  .  .  .  appear  .  .  .  that  the  opposite  sides  of  a  certain 
question  may  be  held  by  persons  not  differing  in  their 
opinion  of  the  matter  in  hand,  then  that  question  may 
be  pronounced  verbal,  as  depending  on  the  different 
senses  in  which  they  respectively  employ  the  terms.     If, 


Chap.  II.]        THE  KINDS  OF  UNREAL  ASSERTION.  145 

on  the  contrary,  it  appears  that  they  employ  the  terms 
in  the  same  sense,  but  still  differ  as  to  the  application  of 
one  of  them  to  the  other,  then  it  may  be  pronounced 
that  the  question  is  real, — that  they  differ  as  to  the 
opinions  they  hold  of  the  things  in  question."  "  If,  for 
instance,"  he  continues,  "two  persons  contend  whether 
Augustus  deserved  to  be  called  a  'great  man,'  then  if  it 
appeared  that  the  one  included  under  the  term  'great' 
disinterested  patriotism,  and  on  that  ground  excluded 
Augustus  from  the  class,  as  wanting  in  that  quality,  and 
that  the  other  also  gave  him  no  credit  for  that  quality, 
but  understood  no  more  by  the  term  'great'  than  high 
intellectual  qualities,  energy  of  character,  and  brilliant 
actions,  it  would  follow  that  the  parties  did  not  differ  in 
opinion,  except  as  to  the  use  of  a  term,  and  that  the 
question  was  verbal.  If,  again,  it  appeared  that  the  one 
did  give  Augustus  credit  for  such  patriotism  as  the  other 
denied  him,  both  of  them  including  that  idea  in  the  term 
great,  then  the  Question  would  be  Real."  In  short,  there 
may  be  a  real  assertion  made  about  a  name  just  as  well 
as  about  any  other  S  ;  and  often  this  is  made  in  so  con- 
fused a  fashion  that  there  is  difficulty  in  seeing  what  is 
intended.  Of  course,  where  two  persons  really  agree 
about  the  actual  qualities  possessed  by  Augustus,  and 
one  says,  '  these  qualities,  good  and  bad  together,  on  the 
whole  entitle  him  to  a  place  in  the  class  of  great  men,' 
while  the  other  says  '  precisely  the  same  qualities  do  not 
entitle  him  to  the  name,'  the  former  really  asserts,  while 
the  latter  denies,  that  (in  their  respective  opinion)  the 


146  FALLACIES.  [Part  II, 

best  meaning  of '  great  *  includes  that  particular  mixture 
of  qualities  which  both  allow  to  belong  to  Augustus. 
But  the  difficulty  in  the  matter  usually  flows  from  the 
fact  that  neither  party  to  the  discussion  knows  very 
clearly  either  what  qualities  he  does  actually  suppose 
Augustus  to  possess,  or  what  qualities  he  does  actually 
include  within  his  meaning  of  the  name.  All  that  we 
are  concerned  to  notice,  however,  is  that  the  confusion — 
if  confusion  there  be — is  not  that  of  mistaking  an  empty 
form  of  words  for  a  real  assertion,  but  of  mistaking  one 
real  assertion  for  another.  The  question  whether  or  no 
a  given  definition  is  a  good  one  may  indeed  be  properly 
called  a  '  verbal  question,'  but  it  is  clearly  not  a  question 
without  meaning  or  without  important  consequences. 
An  assertion  about  the  meaning  of  a  name,  when  under- 
stood as  such,  is  not  a  verbal  assertion  in  the  sense  of 
being  incapable  of  Proof. 

Another  question,  of  side  interest,  may  be  just 
mentioned  for  dismissal.  Since  the  reality  of  an  asser- 
tion is  coincident  with  its  capacity  for  Proof  and  Dis- 
proof, are  we  to  distinguish  degrees  of  *  reality '  according 
to  the  completeness  and  definiteness  of  the  possible  test  to 
which  different  real  assertions  are  liable  ?  It  is  obvious 
that  assertions  vary  very  much  in  this  respect.  Is,  for 
example,  the  assertion,  *  You  will  find  him  in  the  next 
room,'  more  real  (because  more  capable  of  being  brought 
to  a  conclusive  test)  than  an  assertion  regarding  the 
details  of  the  distribution  of  ice  over  Europe  during  the 
last  Glacial  Epoch  ?     Certainly  not.     As  I  have  intended 


Chap.  II.]        THE  KINDS  OF  UNREAL  ASSERTION.  147 

to  use  the  term  '  real '  throughout,  there  are  no  degrees 
in  it, — no  standing-room  between  real  and  unreal.  If  it 
be  desired  to  express  the  distinction  just  spoken  of,  there 
are  other  words, —  such  as  'verifiable' — which  would 
answer  the  purpose  better.  By  '  capacity  for  Proof  and 
Disproof  was  not  meant  the  degree  of  ease  or  certainty 
with  which  the  assertion  might  be  established  or  over- 
thrown, but  the  mere  fact  that  there  is  at  least  no  absolute 
impossibility,  in  the  assertion  itself,  that  relevant  evidence, 
weak  or  strong,  should  ever  be  produced.  The  unreality 
of  a  proposition  is  not  in  any  way  connected  with  the 
mere  inaccessibility  of  Proof  and  Disproof,  but  with  their 
total  inapplicability.  To  establish  or  demolish  some 
'real'  hypotheses  may  be  as  difficult  as  to  establish  a 
dynasty,  or  to  remove  a  mountain;  but  to  support  or 
disprove  an  unreal  proposition  is  as  impossible  as  to 
support  a  dead  Pretender,  or  to  remove  a  hat  from  a  head 
already  bare. 


CHAPTER  in. 

THE  BURDEN  OF  PROOF. 

Supposing  a  Thesis  sufficiently  free  from  the  taint  of 
unreality,  two  other  main  objections  or  opportunities  for 
attack  remain.  And  the  first  of  these,  as  already  said,  is 
the  objection  that  no  proof  has  been  attempted, — that 
the  thesis  is  a  mere  assertion,  standing  entirely  without 
support  or  evidence. 

Evidence,  it  should  be  at  once  noticed,  is  not  here 
used  in  the  more  restricted  sense  that  would  contrast  it 
(e.g.)  with  '  authority '  or  with  '  hearsay ; '  but  as  broadly 
as  possible,  so  as  to  include  the  weakest  kinds  of  evidence 
as  well  as  the  strongest.  It  is  just  as  truly  an  argument, 
for  example,  however  fragile,  to  claim  that  a  given 
assertion  is  true  because  it  occurs  in  a  certain  book,  or 
was  made  by  a  certain  person,  as  any  other  '  reason  given 
for  belief  would  be.  The  contrast  between  supported 
and  unsupported  assertions  does  not  depend  on  the 
strength  or  weakness  of  the  reasons,  but  on  whether 
or  not  reasons  of  any  kind  are  given.  The  full  question 
as  to  the  burden  of  Proof  is  sufficiently  confusing  in 


Chap.  UL]  THE  BURDEN  OF  PROOF.  149 

itself,  without  our  introducing  further  entanglements 
prematurely. 

Two  cases  are  to  be  distinguished: — (1)  Where  an 
assertion  is  put  forward  simply  as  '  self-evident,*  or  free 
from  ail  need  of  Proof;  and  (2)  where  the  assertor 
supposes  (or  tries  to  lead  his  audience  to  suppose)  that 
his  sole  concern  as  assertor  is  to  frustrate,  one  by  one, 
attempts  at  Disproof  made  by  some  one  else. 

The  first  case  need  not  detain  us  long.  For  while 
fully  admitting  that  without  some  '  self-evident '  truths, 
no  Proof  of  any  assertion  would  be  possible,  it  can  hardly 
be  denied  that  what  seems  self-evident  to  one  person 
may  seem  to  another  to  stand  much  in  need  of  external 
support.  And  since  the  whole  meaning  of  the  Need  of 
Proof  is  need  as  felt  hy  the  audience,  and  not  as  the 
assertor  happens  to  think  the  audience  ought  to  feel  it, 
they,  and  not  he,  must  be  the  arbiters.  If  the  assertion 
is  not  to  them  self-evident,  they  are  under  actual  dis- 
ability to  believe  it  until  external  evidence  is  produced. 
I  am  speaking,  of  course,  of  genuine  belief,  intelligent 
and  rational,  and  not  of  mere  voluntary  acceptance  of  a 
formula,  as  an  act  of  obedience  or  otherwise.  It  may, 
indeed,  often  happen  that  the  groimds  are  so  numerous, 
or  have  been  so  long  forgotten  through  disuse,  that  their 
production  would  be  difficult  or  impossible.  Deep-lying 
and  complicated  beliefs,  especially  •when  illumined  by 
emotion,  or  when  the  more  physical  element  in  them 
is  prominent,  are  very  liable  to  this  difficulty, — the 
beliefs  (e.g.)  on  which  our  likes  and  dislikes  of  persons 


150  FALLACIES.  [Pabt  1L 

or  of  systems,  or  of  courses  of  action,  are  founded.  But 
none  the  less  unsatisfactory  must  such  beliefs  remain  to 
an  audience  not  already  convinced,  until  the  grounds 
can  be  openly  brought  forward  and  examined :  and  our 
concern  is,  of  course,  entirely  with  the  point  of  view  from 
which  the  assertion  is  still  a  thesis,  and  not  with  that 
from  which  it  is  a  firmly  established  conclusion.  Until 
the  grounds  can  be  examined  no  test  is  possible:  the 
assertion  may  or  may  not  be  true,  for  all  the  audience 
can  say.  Against  the  honest  objection,  '  This  is  not  self- 
evident  to  me,'  there  is  clearly  no  appeal ;  and  no  remedy 
except  through  the  production  of  real  external  evidence. 

The  second  case,  however,  is  far  more  complicated; 
sufficiently  so,  in  fact,  to  have  notoriously  confused  the 
mind  of  no  less  a  logician  than  Archbishop  Whately.  This 
is  another  of  the  numerous  cases  where  statement  is  easy 
but  application  difficult,  and  where  the  whole  practical 
value  depends  on  the  application.  Stated  shortly, 
the  fundamental  rule  is  that  "He  who  asserts  must 
})rove ; "  *  and  so  long  as  an  assertion  is  undisputed, 
difficulty  cannot  arise.  But  the  chief  source  of  real  per- 
plexity lies  in  attempting  to  keep  a  clear  line  between 
denying  a  thesis,  and  merely  reserving  judgment,-]*  or 

*  Even  in  Law  this  maxim  seems  to  be  fundamental.  Cf.  Sir  Jas. 
Stephen's  Digest  of  the  Law  of  Evidence,  3rd  ed.  pp.  100  ft.  "  The 
burden  of  proof  as  to  any  particular  fact  lies  on  that  person  who  wishes 
the  Court  to  believe  in  its  existence "  (art.  96) .  See  also  Articles  93 
and  95. 

t  Hence  De  Morgan  and  othei-s  have  preferred  to  treat  displacement 
of  the  burden  of  proof  as  a  case  of  Ignoratio  Elenchi.  See  also  the 
examples  at  p.  183  of  this  book. 


Chap.  Ill]  THE  BURDEN  OF  PROOF.  151 

between  disputing  an  argument  and  merely  asking  to 
have  it  expanded  and  made  satisfactory.  This,  at 
least,  is  one  of  the  points  at  which  confusion  is  in  the 
first  place  most  apt  to  creep  in.  It  is  obvious  that  an 
unsupported  assertion  may  or  may  not  be  true,  and  it 
should  be  carefully  noted  that  the  absence  of  produced 
evidence, — or  even  the  absence  of  the  possibility  of  pro- 
ducing evidence, — is  a  very  different  thing  from  Disproof. 
Where  nothing  is  said  either  for  or  against  a  thesis,  its 
truth  simply  remains  an  open  question;  and  where 
nothing  can  be  said,  the  doubt  is  only  more  permanent  in 
character,  not  otherwise  more  triumphant.  The  objection, 
'This  is  bare  assertion,'  does  not  attack  directly  the 
truth  of  the  assertion  in  question,  but  attacks  the  sup- 
position that  such  truth  is  as  yet  established.  Hence 
assertions  which  are  confessedly  mere  suggestions  escape 
unscathed,  since  all  the  harm  which  the  doctrine  of  the 
burden  of  proof  can  do  to  them  is  done  already,  and 
willingly,  by  their  assertor  himself.  It  is  only  where 
an  assertion  is  definitely  made  that  the  grounds  of  belief 
can  be  demanded  with  any  meaning. 

The  simple  statement  of  the  rule,  that  "he  who 
asserts  must  prove,"  needs,  however,  certain  explanations 
before  it  can  be  accepted  in  its  entirety :  and  the  best 
way  to  bring  these  forward  seems  to  be  by  pushing  the 
simple  rule  into  its  extreme  cases.  In  the  first  place, 
then,  if  the  burden  of  proving  lies  always  on  him  who 
asserts,  it  is  clear  that  whoever  asserts  that  a  thesis  is 
false  must  accept  a  burden  too:  and  also  that  he  who 


152  FALLACIES.  [Part  II. 

asserts  a  reason  as  sufficient,  or  claims  that  it  is  certainly 
insufficient,  is  in  exactly  the  same  position.  These  three 
cases  do  not  present  much  difficulty,  and  will,  I  think, 
be  readily  admitted  by  all. 

Suppose,  for  example,  I  assert  some  article  of  popular 
faith, — such  as  that  women  ought  not  to  enter  the 
learned  professions ;  my  audience  may  either  accept  the 
assertion  offhand,  or  deny  it  offhand,  or  be  content  to 
ask  for  reasons.  In  the  first  case  the  burden  passes 
simply  unnoticed.  In  the  second  case,  the  audience,  as 
assertors  accept  a  burden  of  their  own.  In  the  third 
case  the  burden  rests  on  me,  just  as  it  would  if  I  pro- 
claimed the  most  startling  novelty.  For  the  doubt  may 
be  suggested  that  though  widely  believed,  the  assertion 
is  possibly  without  secure  foundation.  That  is  to  say, 
two  courses  are  now  open  to  me — unless  my  audience 
are  unusually  feeble  disputers — either  to  take  my  stand 
on  the  bare  unsupported  assertion,  and  so  leave  my 
questioner  certainly  unconvinced ;  or  else  to  attempt  to 
remove  the  burden  by  producing  the  best  available 
reason.  If  I  adopt  the  latter  course,  it  is  clear  that 
any  permanent  removal  of  the  burden  depends  on  the 
strength  of  the  evidence  brought  forward.  But  the 
difficulty  is,  that  at  every  stage  of  an  argument  the  line 
between  interrogation  and  flat  denial  is  often  hard  to 
preserve,  and  a  sophist,  when  pushed  by  awkward  ques- 
tions, will  always  try  to  shift  the  burden  upon  his 
questioner.  Thus,  I  may  perhaps  argue,  in  favour  of 
women's  restrictions,  that  "one  needs  to  know  that  a 


Chap.  III.]  THE  BURDEN   OF   PROOF.  153 

given  innovation  is  not  dangerous,  before  proceeding  to 
say  confidently  that  the  time  has  come  when  it  may 
be  made."  Very  true,  but  I  am  now  shifting  my  own 
ground,  and  trying  to  fasten  on  my  questioner  a  positive 
assertion  which  he  has  never  made.  I  have  quite  ignored 
the  third  alternative  that  lies  between  'saying  confidently 
that  the  time  has  come '  and  my  own  equally  confident 
original  assertion  that  such  time  has  not  yet  arrived; 
namely,  the  alternative  of  holding  my  tongue,  or  at  least 
of  softening  assertion  into  mere  suggestion  and  asking 
modestly  to  hear  the  possible  objections.  If  my  opponent 
understands  the  doctrine  of  the  burden  of  proof,  he 
naturally  proceeds  to  point  out  my  mistake.  We  need 
not  develop  this  particular  argument  any  further,  since 
enough  has  been  shown  to  illustrate  the  point  imme- 
diately before  us.  Whatever  reasons  I  may  produce,  so 
long  as  difiiculties  in  seeing  their  cogency  are  genuinely 
felt,  it  is  clearly  my  concern  to  remove  them  if  I  can. 

Secondly,  it  seems  undeniable  that  even  the  most 
cautious  sceptic  cannot  escape  a  certain  responsibility. 
The  burden  of  proof  must  rest  on  him  who  asserts  that 
an  assertion  is  doubtful,  just  as  much  as  on  him  who 
asserts  it  true  or  untrue.  But  two  very  difierent  mean- 
ings may  be  distinguished,  in  calling  an  assertion 
doubtful, — the  one,  that  I  (the  objector)  feel  a  doubt; 
the  other,  that  you  (the  assertor)  ought  to  feel  one.  If 
I  merely  intend  the  former  of  these  two  meanings,  my 
responsibility  (which  may  still  be  fully  admitted)  applies 
not  at  all  to  the  point  at  issue,  but  to  a  matter  of  side- 


154  FALLACIES.  [Part  IL 

interest, — the  question  whether  I  am,  or  am  not,  honest 
in  making  the  demand.  It  is  conceivable  that  I  shall 
not  take  any  pains  at  all  to  avoid  the  imputation  of 
quibbling.  The  sceptic  may  in  general  be  more  easily 
content  to  leave  the  other  side  alone.  We  are  seldom  as 
anxious  to  prove  our  ignorance  or  obtuseness  as  to  prove 
our  knowledge  or  insight,  and  hence  the  sceptic  may 
cheerfully  neglect  such  burden  as  falls  on  him.  And,  in 
any  case,  the  course  he  chooses  to  take  in  this  matter 
does  not  affect  the  point  at  issue  between  the  parties. 

Lastly,  it  follows  that  even  he  who  asserts  the  most 
widely  accepted  doctrine  cannot  escape  the  '  burden '  of 
supporting  it  by  reasons.  The  burden  of  proof  rests,  for 
example,  on  those  who  maintain  the  theory  of  gravitation 
or  of  the  rotundity  of  the  earth,  just  as  truly  as  on  any 
one  who  should  set  up  for  his  thesis  the  denial  of  either  : 
the  difference  is  that  in  asserting  such  truths  as  these  the 
burden  is  apt  to  pass  unnoticed,  from  the  fact  that  the 
evidence  is  strong  enough  to  shift  it  easily,  while  in 
denying  them  the  burden  might  really  be  felt  as  a 
serious  weight.  And  this  leads  us  to  speak  of  the  chief 
practical  difficulty  in  the  matter,  —  the  point  where 
Practice  demands  that  inquiry  shall  be  stifled. 

Whately's  doctrine  of  the  burden  of  proof*  was 
brought  forward,  as  his  readers  will  remember,  partly  for 
the  purpose  of  annihilating  Infidelity  by  a  short  and 
easy  method :  but  it  is  none  the  less  worth  considering 
in  itself,  since  the  confusion  into  which  he  fell  is  a  very 
♦  Rhetoric:  Part  i.  chap.  ill.  §  2. 


Chap.  IH.]  THE  BURDEN  OF  PROOF.  155 

excusable  one,  though  probably  not  often  effective  against 
the  more  modern  kind  of  Infidel.  "  There  is  a  Presump- 
tion "  he  writes  "  in  favour  of  every  existing  institution  " 
.  .  .  "Christianity  exists;  and  those  who  deny  the 
divine  origin  attributed  to  it  are  bound  to  show  some 
reason  for  assigning  to  it  a  human  origin."  Of  course, 
there  is  "  a  presumption  in  favour  of  any  existing  institu- 
tion." Since  it  already  exists,  any  one  wishing  to  abolish 
or  alter  it  must,  of  course,  in  the  first  place  make  an 
assertion  to  that  effect,  and  also  produce  his  reasons, — 
or  else  nothing  will  probably  be  done.  But  a  pre- 
sumption of  this  kind  is  a  very  different  thing  from  a 
presumption  that  an  assertion  made  by  an  existing 
institution  is  true.  Various  forms  of  Paganism  exist; 
are  we  therefore  to  believe  without  inquirj'-  whatever 
their  followers  may  choose  to  assert  about  them  ?  No 
doubt  this  verbal  ambiguity  was  complicated  also  with 
another  confusion, — that  between  denying  and  qv£stion- 
ing  the  divine  origin  of  the  institution :  the  Archbishop 
very  naturally  failed  to  put  himself  exactly  in  the  position 
of  a  real  unbeliever,  and  was  considering  only  the  case 
of  one  who  should  set  out  to  prove  to  a  believer  that 
his  belief  was  misplaced.  In  such  a  case  certainly  the 
burden  would  in  the  first  place  lie  on  the  infidel,  as 
being  the  person  making  the  assertion.  But  it  is  surely 
not  often  that  infidels  are  so  generous.  Or  rather,  to 
put  it  more  fairly,  they  have  not  .the  same  reason  to  be 
anxious  to  convert  believers  as  the  latter  have  (ad- 
mittedly) to  convert  them, — since  no  infidel  pretends  to 


156  FALLACIES.  [Pabt  IL 

believe  that  a  Christian  will  miss  incalculable  benefits  on 
account  of  his  Christianity.  Hence  it  is  the  unbelievers 
who  really  take  the  unassertive  position,  not  professing 
to  have  any  valuable  information  on  the  points  directly 
in  question,  which  information  they  are  eager  to  impress 
on  the  other  side ;  but  quietly  willing  to  examine  (with 
minds,  at  least  professedly,  open  and  candid)  any  asser- 
tions brought  forward  and  supported.  It  is  the  believer 
whose  mind — even  on  his  own  showing — is  no  longer 
open :  he  it  is  who  claims  to  have  already  weighed  all 
the  arguments  and  arrived  at  a  firm  decision;  who 
claims  the  possession  of  valuable  information  which  he 
is  burning  to  impart, — information  so  valuable  that, 
except  on  the  plea  of  extreme  difficulty  in  producing 
unexploded  reasons,  it  seems  almost  cruelty  on  his  part 
to  be  content  with  bare  assertion.  Certainly,  any  one  who 
should  set  up,  to  a  believer,  the  thesis  'Christianity 
is  of  purely  human  origin'  must  bring  forward  his 
reasons  for  that  thesis,  or  else  expect  the  believer  to 
remain  unshaken :  but  on  the  other  hand  any  one  who 
sets  up,  to  an  unbeliever,  the  thesis  '  Christianity  is  of 
divine  origin '  is  in  exactly  the  same  position.  Professed 
ignorance,  however  often  a  mere  pretence,  and  however 
often  (when  real)  a  sign  of  culpable  indifference  or  of 
pitiable  want  of  power,  is  also  the  natural  and  normal 
position  of  the  anxious  mind,  until  anxiety  is  removed  by 
the  production  of  evidence  that  at  least  seems  sufficient. 

And  here  it  seems  in  place  to  notice  that  the  real 
difficulty  as  to  the  burden  of  proof  is  somewhat  deeper 


Chap.  UI.]  THE  BURDEN  OF  PROOF.  157 

and  more  serious  than  might  be  supposed  either  from 
a  bare  statement  of  the  fundamental  rule,  or  from  a 
rough  description  of  the  cautious  attitude  in  one  or 
two  rather  artificial  controversies.  In  Logic  altogetlier 
there  is  often  a  danger  of  treating  words  as  more  than 
counters,  and  so  of  giving  an  air  of  wordiness  and 
trickery  to  the  results  attained ;  and  in  all  this  matter 
of  the  burden  of  proof  the  danger  in  question  is  perhaps 
especially  active.  It  is  not  only  in  disputes  and  verbal 
arguments  that  the  correct  placing  of  the  burden  is 
important,  but  wherever  we  are  called  upon  to  judge 
whether  aU  objections  to  an  assertion  have  been  properly 
taken  into  account;  as  where,  for  instance,  we  have  to 
decide  between  accepted  theory  and  awkward  fact.  The 
diflBculty  at  last  resolves  itself  into  that  of  saying  what 
shall  constitute  '  practically  conclusive '  prejudice. 

How  far,  for  example,  are  we  'bound  to  explain 
away '  a  so-called  fact  ?  If  we  already  have  an  ap- 
parently well-established  theory  regarding,  say,  the 
impossibility  of  corpses  reviving,  or  of  '  spirits '  holding 
communication  with  the  living,  or  even  if  our  theory 
goes  no  further  than  to  deem  some  given  behaviour 
of  mind  or  matter  a  physical  impossibility,  what  is  the 
rational  attitude  towards  a  claimed  miracle,  or  ghost- 
story,  or  mere  narration  of  marvellous  fact  for  which  no 
explanation  is  offered  ? 

We  need  not  now,  of  course,  hesitate  at  any 
purely  verbal  obstacle.  We  may  say,  if  we  like,  that 
the  bare  notion  of  a  'miracle'  involves  a  contradiction 


158  FALLACIES.  [Part  IL 

in  terms ;  this  merely  means  that  if  we  were  sufficiently 
wise  there  would  be  no  room  for  wonder.  But  that  the 
blind  should  receive  their  sight  in  an  unexpected  manner, 
or  that  a  conjuror's  performances  should  lie  beyond  our 
powers  of  explanation,  involves  no  contradiction  or  im- 
possibility, except  on  the  assumption  that  we  have 
already  exhausted  all  there  is  to  learn.  When  Mr. 
Venn  *  says  that  "  few  men  of  any  really  scientific  turn 
would  readily  accept  a  miracle,  even  if  it  appeared  to 
happen  under  their  very  eyes,"  what  is  meant  is  that, 
though  surprised  at  first,  they  would  either  "  soon  come 
to  discard  it  afterwards,  or  so  explain  it  away  {i.e.  bring 
it  under  known  laws)  as  to  evacuate  it  of  all  that  is 
meant  by  miraculous." 

The  rough  and  ready  doctrine  may  be  called  that 
of  the  existence  of  '  fair  presumptions,'  whether  left 
indefinite,  as   in   common    parlance,!    or — as  in  law — 

•  Logic  of  Chance,  p.  450. 

t  And  perhaps  in  Science.  Thus  Professor  Tyndall,  in  epeaking 
{Floating  Matter  of  the  Air,  p.  305)  of  the  experiments  to  disprove 
Spontaneous  Generation,  claims  that  whereas  life  in  the  sealed  test- 
tube  may  always  be  due  to  errors  of  manipulation,  the  absence  of  life 
"  involves  the  presumption  of  correct  experiment."  The  difference 
between  scientific  'presumption'  and  unscientific  is,  however,  worth 
noting.  By  this  claim  it  is  not  meant  that  a  single  failure  to  find  life 
in  certain  conditions  is  sufficient  at  once  to  remove  all  doubt :  the 
patience  with  which  Professor  Tyndall's  own  full  investigation  was 
conducted  bears  witness  to  the  contrary.  But  it  is  merely  claimed  that 
where  the  instances  for  and  against  are  equal  in  number,  the  evidence 
is  "  not  equally  balanced,"  and  that  "  as  regards  the  fruitful  flaska 
[a  careful  inquirer]  would  .  .  .  repeat  the  experiment  with  redoubled 
care  and  scrutiny,  and  not  by  one  repetition  only,  but  by  many,  assure 
himself  that  he  had  not  fallen  into  error." 


Chap.  HI.]  THE  BURDEN  OF  PROOF.  159 

defined  to  some  extent  by  set  rules.  It  amounts,  in 
brief,  to  this,  that  where  there  exists  a  '  fair  presumption  * 
in  favour  of  a  belief,  or  where  a  belief  is  in  harmony 
with  prevailing  opinion,  the  assertor  is  not  *  bound '  to 
produce  evidence,  but  that  whoever  doubts  the  assertion 
is  bound  to  show  cause  why  it  should  not  be  believed. 
The  value  of  this  procedure,  as  a  short  cut  or  as  a  weapon 
agahist  mere  obstruction,  must  be  apparent  at  once.  A 
Law  Court,  for  example,  one  of  whose  unavoidable  limi- 
tations seems  to  be  the  occasional  necessity  of  sacrificing 
the  individual  to  the  average — i.e.  of  resting  content  with 
caring  not  at  all  about  the  minima  of  justice — may  derive 
on  the  whole  great  advantage  from  such  special  rules,  at 
any  rate  as  regards  speed  in  getting  through  its  work. 
Thus,  a  person  found  in  possession  of  stolen  goods  soon 
after  the  theft,  is  presumed  to  be  the  thief,  and  has  to 
prove  innocence  although  he  is  the  accused  party.  If 
a  married  woman  in  this  awkward  situation  proves  that 
she  stole  the  goods  in  the  presence  of  her  husband,  but 
asserts  that  he  compelled  her  to  steal  them,  she  escapes 
the  burden  of  proving  this  latter  assertion,  since  the  Law 
considers  it  self-evident.*  And  every  rule  that  dictates 
in  general  how  given  facts  or  admissions  shall  be  con- 
strued, is  an  example  of  this  procedure.  Convenient,  how- 
ever, as  such  a  plan  may  be  where  there  is  an  authority 
competent  to  frame  the  rules,  it  is  obvious  that  out- 
side  certain   artificial  institutions,   existing    for    some 

•  Cf.  Stephen.    Digest  of  the  Law  of  Evidence.    Articles  95  and  96. 
Cf.  also  De  Morgan :  Formal  Logic,  p.  261. 


160  FALLACIES.  [Pabt  IL 

special  purposes,  no  such  authority  exists.  Argument 
in  general  cannot  undertake  to  be  bound  by  what  this 
man  or  the  other,  or  any  body  of  men,  may  happen  to 
consider  a  '  fair  presumption.'  Logic  shrinks  into  mere 
cleverness  under  the  bondage  of  Rules  for  Debate,  and 
dogma  cramps  the  reasoning  powers.  If,  as  Whately 
claimed,  those  who  put  forward  assertions  in  harmony 
with  '  prevailing  opinion '  were  to  be  altogether  exempt 
from  giving  a  reason  for  the  faith  that  is  in  them,  or 
if  those  who  bring  forward  facts  in  opposition  to  pre- 
vailing opinion  were  to  be  thereby  ruled  out  of  court 
at  once,  with  whom  would  rest  the  right  of  deciding  what 
assertions  and  facts  really  come  within  such  privilege  ? 
Even  an  Archbishop,  it  must  be  acknowledged,  might 
fail  to  catch  the  precise  moment  when  a  struggling  truth 
really  begins  to  '  prevail : '  and  ordinary  folk,  who  only 
desire  to  follow  the  safest  leader,  have  often  the  greatest 
possible  difficulty  in  deciding  which  party  shall  claim 
their  allegiance  and  support.  At  least  it  might  very 
well  happen  that  any  two  people  should  fail  to  agree 
as  to  what  is  the  prevailing  opinion, — much  more,  as  to 
what  it  ought  to  be.  Perhaps  then  we  must  rely  upon 
the  submissiveness  of  our  audience  ?  Such  a  view  comes 
near  being  an  'Idol  of  the  Cave.'  Rather,  it  should 
perhaps  be  called  an  Idol  of  the  Hothouse, — a  tender 
plant,  that  can  never  thrive  long  in  the  open  air. 

Common-sense  has,  of  course,  a  very  justifiable  liking 
for  short  cuts  wherever  practicable.  Rough  and  ready 
rules    for    interpreting   facts    have   a   value    certainly. 


Chap.  III.]  THE  BURDEN  OF  PROOF.  161 

even  outside  a  Court  of  Justice.  But  there  is  all  the 
difference  between  using  these  as  our  servants,  and 
allowing  them  to  become  our  masters.  So  long  as  they 
are  employed  confessedly  as  a  mere  apparatus  for  saving 
time  at  the  cost  of  some  exactness,  no  harm  is  done  :  for 
where  the  thesis  is  more  than  usually  important  we  can 
take  more  than  the  usual  care.  But  if  we  suppose  that 
whenever  a  bold  assertor  takes  refuge  behind  his  two- 
thirds  majority,  the  spirit  of  free  inquiry  ought  at  once 
to  apologise  tamely  for  having  dared  to  put  awkward 
questions  or  to  bring  forward  awkward  facts,  we  have  only 
ourselves  to  blame  for  the  loss  we  suffer.  The  assertor 
who  shirks  inquiry  can  always  be  shown  to  be  shirking, 
by  the  simple  process  of  putting  the  question  clearly  and 
letting  others  see  that  it  remains  unanswered. 

Both  the  practice  of  relying  on  prevailing  opinion 
then,  and  also  readiness  in  accepting  subversive  facts  as 
undeniable,  have  a  double  edge,  and  need  a  little  care 
in  using.  If  Science  lays  down  a  theory,  or  Guess- 
work a  doctrine,  conflicting  facts  or  probing  questions 
may  both  be  awkward.  But  a  question  differs,  after  all, 
from  an  asserted  '  fact '  in  one  very  important  particular, 
— it  carries  no  burden  itself  A  '  fact '  stands  in  need  of 
evidence,  whether  or  no  it  conflicts  with  theory:  and 
clearly,  the  firmer  the  theory  the  greater  the  caution 
required  in  accepting  evidence  for  the  conflicting  fact. 
We  find,  no  doubt,  very  often,  that  the  ease  (or  difiiculty) 
with  which  a  '  fact '  is  accepted  depends  more  on  pre- 
judice against  (or  for)  a  given  theory  than  on  the  presence 


162  FALLACIES.  [Part  IL 

(or  absence)  of  undeniable  support  for  the  fact  itself:  but 
even  where  the  fact  does  rest  on  evidence  of  its  own, 
we  should  not  forget  that  in  judging  that  evidence 
also  there  is  involved  a  very  large  amount  of  rough 
and  ready  presumption ;  that  in  all  observation  there  is 
involved  a  certain  amount  of  inference.  To  say  that  the 
supporter  of  a  theory  is  in  any  way  '  bound  to  explain 
away'  a  given  supposed  fact,  may  be  just  as  high-handed 
a  proceeding  as  for  the  theorist  to  condemn  the  fact 
unheard.  It  must  be  proved  to  be  a  fact  before  it  has 
any  bearing  on  the  theory;  otherwise,  it  is  clearly  a 
case  of  "so  much  the  worse  for  the  facts."  There  can 
thus  be  no  law  laid  down  which  shall  settle  aU  disputed 
cases  a  priori:  we  can  only  come  back,  after  all,  to 
the  one  fundamental  principle  that  wherever  proof  is 
demanded,  we  must  either  be  prepared  with  sufficient 
evidence,  or  prepared  to  see  the  hopeful  proselyte  un- 
convinced. 

Shortly,  we  may  sum  up  the  worst  of  the  difficulties 
surrounding  the  question  as  to  the  burden  of  proof  as 
due  partly  to  the  unfortunate  ambiguity  of  the  expres- 
sion itself,  and  partly  to  an  endless  source  of  trouble, — 
the  practical  need  of  striking  some  balance  between  faith 
and  hesitation.  The  mere  ambiguity  of  the  expression 
may  be  met  by  remembering  that  the  *  must '  of  the  rule 
is  only  sanctioned  by  the  assertor's  eagerness  to  convince 
his  audience ;  and  that  to  '  assert '  must  therefore  be 
defined  to  exclude  that  milder  t3^e  of  assertion  where 
we  either  state  an  opinion  as  a  fact  in  our  mental  history. 


Chap.  III.]  THE  BURDEN  OF  PROOF.  163 

or  tentatively  and  with  a  view  to  learning  what  the 
objections  to  it  really  are. 

In  Logic,  then,  when  we  speak  of  the  burden  of  proof, 
we  are  not  speaking  of  some  artificial  law, — some  merely 
legal,  or  perhaps  Parliamentary  rule, — with  artificial 
penalties  attached  to  it.  No  doubt  much  that  has  been 
written,  even  in  logical  works,  has  been  written  with 
some  such  view.  For  centuries  after  Aristotle's  time, 
argument  appears  to  have  been  regarded  as  a  kind  of 
intellectual  game,  in  which  each  player  might  try  to 
obtain  what  advantage  he  could,  so  long  only  as  he 
obeyed  the  rules  laid  down.  The  microscopic  ingenuity 
with  which  the  Schoolmen  carried  on  the  elaboration  of 
these  rules  was  well  worthy  of  a  better  object.  But  here, 
at  any  rate,  we  are  free  from  any  such  limitations.  No 
penalty  follows  the  misplacement  of  the  burden  of  proof, 
in  the  strict  sense  in  which  we  here  use  the  expression, 
except  the  natural  consequence  that  the  assertion  remains 
untested,  and  the  audience  therefore  (if  inquiring)  un- 
convinced. To  lay  the  burden  on  another,  therefore, 
is  not  to  demand  Proof  at  the  point  of  the  sword,  but 
rather  to  request  it  as  a  favour.  There  is  no '  obligation ' 
on  any  one  to  prove  an  assertion, — other  than  any  wish 
he  may  feel  to  set  an  inquiring  mind  at  rest,  or  to  avoid 
the  imputation  of  empty  boasting.  It  is  a  natural  law 
alone  with  which  we  are  here  concerned, — the  law  that 
an  unsupported  assertion  may,  for  all  that  appears,  be 
either  true  or  false.  And  a  corollary  is  that  the  more 
intelligent  the  audience  the  less  easy  will  it  be  to  pass 


164  FALLACIES.  [Part  IL 

off  upon  them  a  bare  assertion  under  the  pretence  that 
they  are  in  any  way  '  bound '  to  disprove  it  or  explain 
it  away. 

And,  as  regards  the  practical  need  of  recognising  fair 
presumptions,  the  best  key  seems  to  be  to  keep  quite 
clear  the  fine  distinction  between  two  really  different 
doctrines ;  one,  the  firm  foundation  of  all  the  cogency 
that  Proof  can  ever  attain,  and  the  other  the  tottering 
shelter  for  boastfulness  that  fears  to  be  found  out.  The 
former  may  be  described  as  the  doctrine  that  before  we 
can  safely  accept  a  given  theory  we  are  bound  to  discard 
all  possible  rival  ones :  the  latter  the  doctrine  that  before 
we  can  presume  to  decline  to  accept  a  given  theory,  we 
are  bound  to  provide  an  efficient  substitute.  Nakedly 
stated  like  this,  perhaps,  their  difference  is  easy  enough 
to  see,  but  there  are  aspects  (or  uses  to  which  they  may 
be  put)  under  which  they  become  rather  more  difficult  to 
keep  distinct.  Thus,  for  example,  a  theory  occurs  to  us 
as  satisfactory,  and  instead  of  actively  trying  to  find  out 
all  that  can  be  said  against  it,  or  what  rival  theories  are 
possible,  we  entitle  it  a  '  provisional  theory,'  or  a  '  work- 
ing hypothesis,'  and  then  proceed  at  once  to  dismiss  all 
doubts  from  our  mind.  I  am  not,  of  course,  saying  that 
this  provisional  contentment  is  always  to  be  avoided, — 
only  that  there  is  more  of  it  in  circulation  than  would, 
perhaps,  be  the  case  if  our  notions  of  the  burden  of  proof 
were  kept  quite  clear.  The  inclination  to  believe  without 
inquiry  has  long  ago  become  a  confirmed  habit  of  the 
human  race;   dating,  no   doubt,  from  the  times  when 


Chap,  ni.]  THE  BURDEN  OF  PROOF.  165 

sheer  necessity — poverty  of  knowledge — led  us  to  invent 
our  facts :  while  the  use  of  provisional  theories  as  such, 
i.e.  with  full  recognition  of  their  imperfections,  seems  to 
be  an  art  which,  with  all  our  good  intentions,  we  are 
only  slowly  learning. 

Further,  since  where  no  Reason  is  given  the  Thesis 
may  be  either  true  or  false,  a  second  corollary  is,  as  already 
noted,  that  the  absence  of  a  reason  given  is  no  conclusive 
condemnation  of  the  assertion  made.  Whether  it  should 
even  raise  a  presumption  of  weakness  depends,  of  course, 
on  circumstances.  It  would  not  do  so,  for  example, 
where  the  assertor,  without  any  motive  for  untruth,  is 
merely  relating  unmistakable  facts  within  his  own  ex- 
perience,— as  that  he  came  down  by  the  Midland  Rail- 
way, or  that  he  usually  buys  his  books  at  a  certain  shop. 
As  a  broad  rule,  in  fact,  we  might  say  that  the  need  for 
proof  depends  on  three  classes  of  circumstances, — the 
likelihood  of  mistake,  the  likelihood  of  falsification,  and 
the  importance  of  the  assertion  made.  Where  all  three 
of  these  are  at  a  minimum,  the  need  for  proof  is  at  a 
minimum  too:  where  any  one  of  these  rises  into  pro- 
minence, the  demand  for  proof  begins.  Thus  the  asser- 
tions (1)  that  I  saw  a  ghost,  or,  (2)  that  defendant  was 
elsewhere  at  the  time  the  deed  was  committed,  or,  (3) 
that  the  earth  will  be  baked  to  a  cinder  in  1897,  would 
be  generally  felt  to  stand  in  need  of  evidence.  Closely 
bound  up  with  the  need  of  Proof  is,  of  course,  the  pre- 
sumption of  weakness  which  its  continued  absence  is  apt 
to  raise.    That  is  to  say,  where  the  need  is  strong  the 


166  FALLACIES.  [Pabt  IL 

call  is  usually  audible ;  and  deafness  is  known  to  be  often 
largely  voluntary.  But  so  far  as  appears,  no  general 
rule  can  be  framed  for  judging  of  the  strength  of  such 
presumption  in  a  given  case.  Even  distinct  unwilling- 
ness to  produce  the  grounds  of  belief  is  an  ambiguous 
sign, — much  more  so  is  the  mere  absence  of  evidence, 
however  strong  the  call  for  Proof  Unquestioning  faith, 
for  example, — the  failure  to  see  any  necessity  for  ex- 
amining the  grounds — is  often  a  cause  of  unsupported 
assertion.  So  is  the  simple  desire  to  avoid  trouble.  So 
is  distrust  of  our  audience.  So  again,  as  already  noticed, 
are  the  mere  number  and  extent  of  the  reasons,  and  our 
fear  of  failing  to  do  them  justice.  Insecure  faith — the 
fear  of  losing  the  belief  if  strict  inquiry  should  be  made — 
is  only  one  cause  among  many :  nor,  even  if  it  were  the 
sole  explanation  of  such  unwillingness,  would  the  sign  be 
beyond  dispute.  For  misplaced  timidity  in  our  beliefs 
is  not  altogether  unknown. 

Much  the  same  applies  to  the  case  where  the  assertor 
does  produce  evidence,  time  after  time — either  old  argu- 
ments or  new  ones — and  yet  every  time  such  evidence  is 
found,  by  the  best  tests  obtainable,  to  be  insuflGicient. 
The  practical  difficulty  is  that  of  saying  where  our  rooted 
distrust  shall  begin.  The  failure  of  argument,  however 
long  continued,  never  indeed  amounts  to  conclusive  dis- 
proof; since  either  the  real  difficulty  in  producing  the 
sufficient  grounds,  or  the  assertor's  want  of  skill,  may  be 
to  blame.  But  it  can  hardly  be  denied  that  the  pre- 
sumption does  in    certain  cases    become    very  strong 


Chap.  III.]  THE  BURDEN  OF  PROOF.  167 

indeed, — quite  sufficiently  so  for  many  rough  practical 
purposes.  Since,  however,  there  does  not  yet  appear  to 
be  any  means  of  generalising  the  cases  satisfactorily,  it 
seems  best  only  to  notice  this  as  a  standing  difficulty  in 
the  complete  practical  theory  of  Proof,  at  present  beyond 
the  reach  of  anything  more  definite  than  what  may  be 
called  a  kind  of  logical  tact.  It  is,  however,  a  side  issue, 
and  does  not  afiect  the  'burden  of  proof  itself 

It  is  quite  possible,  therefore,  to  be  over-pedantic  or 
vexatiously  unpractical,  in  demanding  Proof,  just  as  in 
demanding  explanation  of  the  meaning  of  a  term.  And 
in  this  case  as  in  the  former  the  question  whether  a  given 
demand  is  on  the  whole  conducive  to  the  interests  of 
practice  may  indeed  itself  be  raised  and  answered,  but 
otherwise  lies  quite  outside  the  scope  of  our  inquiry. 
In  strictness  any  assertion  may  have  its  grounds  called 
for;  and  until  they  are  produced  and  examined,  the 
assertion  remains  untested.  Whether  practical  con- 
venience decides  that  in  certain  cases  the  assertion  may 
safely  be  left  in  this  state,  is  another  matter.  "We  are 
only  concerned  with  those  assertions  which  are  already 
erected  into  theses;  i.e.  which  have,  in  the  opinion 
(mistaken  or  not)  of  the  audience,  sufficient  importance 
and  doubtfulness  to  make  proof  desirable  and  demanded. 


SECTION  II.— NON   SEQUITUR. 
CHAPTER  IV. 

INTEODUCTORY. 

When  a  real  assertion  is  made,  and  reasons  of  some  sort 
given  for  believing  it,  such  reasons  may  perhaps  be 
inadequate  as  a  guarantee.  In  a  former  chapter  (p.  102) 
it  was  noticed  that  all  the  dangers  in  accepting  any 
Reason  as  evidence  for  any  Thesis,  may  be  reduced  to 
the  two  main  heads,  (1)  Failure  in  formal  adequacy,  and 
(2)  Failure  in  material  truth,  of  such  Reason ;  and 
further,  that  the  first  of  these  departments  is  the  only 
one  that  needs  analysis  in  Logic.  Non  sequitur  is  thus 
co-extensive  with  failure  in  the  formal  adequacy  of  the 
Reason. 

We  here  reach  what  may  be  considered  the  centra] 
and  most  important  part  of  the  whole  subject,  and  the 
part  which  certainly  presents  by  far  the  greatest 
difficulties.  The  chief  source  from  which  these  difficulties 
flow  is  one  whose  influence  is  not  confined  to  Logic,  but 
is  felt  more  or  less  in  all  departments  of  knowledge, — 
the  need  for  compromise  between  the  completest  possible 


Chap.  IV.]  INTRODUCTORY.  169 

investigation  and  a  sufficient  degree  of  speed  in  practice. 
It  seems  to  be  inevitable  that  in  applying  Logic  some 
compromise  between  these  conflicting  desiderata  should 
be  made :  all  that  can  be  done  is  to  recognise  the  com- 
promise as  such,  keeping  a  jealous  guard  against  un- 
justified encroachments,  yielding,  of  course,  where  it  can 
be  seen  that  the  gain  is  worth  the  price,  but  in  such 
cases  remembering  always  that  a  certain  risk  is  being 
run. 

To  speak  less  generally,  the  main  difficulty  against 
which  any  methods  for  the  accurate  detection  of  Fallacy 
have  to  contend  is  the  convenient  practice  of  employing 
guesswork.  In  many  cases  it  is  possible  to  see  at  a 
glance,  with  quite  sufficient  accuracy,  what  the  cause  of 
the  fallacy  has  been ;  and  it  is  then,  perhaps  rightly,  felt 
as  a  waste  of  time  to  set  about  the  search  in  any  lengthy 
painstaking  fashion.  When,  for  instance,  such  an  argu- 
ment is  met  with  as  that  "  we  ought  to  be  guided  by  the 
decisions  of  our  ancestors,  for  old  age  is  wiser  than 
youth,"  even  the  most  cautious  person  can  hardly  help 
feeling  a  high  degree  of  security  in  guessing  that  the 
operative  cause  has  been  some  misinterpretation  of  the 
meaning  of  Reason  or  Thesis  or  both,  whereby  the  full 
difference  between  '  ancestors '  and  '  persons  old  in  age ' 
has  been  overlooked.  So  again  where  we  find  it  argued 
that '  every  effect  must  have  had  a  cause,  since  otherwise 
it  would  not  be  an  effect,'  we  are,  no  doubt,  justified  in 
suspecting  some  attempt  to  argue  in  a  circle.  So  in  a 
considerable  number  of  cases  Common  Sense  can  lay  a 


170  FALLACIES.  [Part  IT. 

finger  at  once  on  the  cause  of  the  fallacy,  and  thus  go  to 
the  root  of  the  matter  without  elaborate  inquiry. 

A  very  little  inspection  of  actual  instances,  however, 
will  show  that  this  is  far  from  being  always  so  easy. 
The  causes  of  Non  sequitur  are  manifold,  and  in  the 
large  majority  of  cases  the  same  false  argument  may  be 
due  to  one  of  several ;  and  these,  morever,  not  necessarily 
acting  in  isolation,  but  as  a  rule  two  or  three  combining 
to  establish  a  false  belief.  A  given  fallacy  may  be  partly 
due  to  misinterpretation  of  language,  partly  to  forgetful- 
ness  of  logical  principles,  partly  to  incomplete  analysis  of 
facts  observed,  and  so  on :  the  union  of  causes  often  makes 
their  strength.  Whether  or  no  it  is  these  difficulties, 
however  indistinctly  felt,  that  have  led  several  writers 
to  declare  the  systematic  treatment  of  fallacies  to  be 
altogether  hopeless,  at  any  rate  the  facts  have  been  dis- 
tinctly recognised  and  deplored  by  others.  Whately,  for 
instance,  writes,  "  It  must  often  be  a  matter  of  doubt,  or 
rather  of  arbitrary  choice,  not  only  to  which  genus  each 
kind  of  fallacy  should  be  referred,  but  even  to  which  kind 
to  refer  any  one  individual  fallacy."  And  he  further 
speaks  of  the  "utter  impossibility"  of  framing  any 
classification  which  shall  be  completely  secure  from  this 
objection.  Mill  endorses  Whately's  opinion,  but  intro- 
duces into  his  own  list  of  fallacies  one  class — those  of 
Confusion — under  which  he  says,  "almost  all  fallacies 
might  in  strictness  be  brought.  ...  A  fallacy  can  seldom 
be  absolutely  referred  to  any  of  the  other  classes."  The 
outcome  of  all  which  is,  that  it  is  very  easy  to  give  an 


Chap.  IV.]  INTRODUCTORY.  171 

actual  case  of  fallacy  a  wrong  name,  very  difficult  (hope- 
less except  by  means  of  special  knowledge  of  the  circum- 
stances) to  be  sure  that  we  have  named  it  rightly ;  and 
quite  impossible  to  guarantee  that  even  the  honest 
fallacious  reasoner  can  be  made,  in  this  way,  to  see  his 
error.  We  are  led  then  to  recognise  'Plurality'  (and 
combination)  of  causes  of  Non  sequitur  as  a  fact,  and  to 
admit  that  any  attempt  to  determine  what  has  misled 
another  person  is  open  to  exactly  the  same  risks  and 
difficulties  as  any  other  attempt  to  read  our  neighbours' 
thoughts  or  motives. 

What  is  meant  b}'-  classifying  Fallacies  or  classifying 
anything?  All  classes  whatever  are  formed  not  by 
'  Nature '  only,  but  by  ourselves  reviewing  the  facts  pre- 
sented there,  and  wishing  to  sum  them  up  conveniently 
for  pui-poses  of  our  own.  Finding  some  point  of  resem- 
blance between  A,  and  B,  and  C,  .  .  .  we  give  them  a 
common  name,  and  thereby  erect  them  into  members  of 
the  class  which  the  name  denotes.  This  is  never  done 
without  a  purpose,  however  dimly  conceived ;  and  such 
purpose  is,  ultimately,  always  the  comparison  of  new  cases 
with  those  already  known.  Just  where  the  possibility  of 
identifying  instances  ceases,  the  value  of  any  classi- 
fication ceases  too.  The  whole  purpose  of  framing  classes 
of  fallacy  is  to  enable  us  to  compare  any  new  instance 
of  faulty  argument  with  others  already  known  to  be 
fallacious, — if  possible  with  the  most  simple  and  naked 
example  of  the  class.  And  if  our  classes  be  such  that 
the  identification  of  actual  instances  is  "a  matter  of 


172  FALLACIES.  [Part  IL 

doubt  or  rather  of  arbitrary  choice,"  6r,  as  Mill  puts  it, 
if  men's  actual  errors  will  not  always  or  even  commonly 
fall  into  our  classes,  the  preservation  of  the  names 
(unremedied  and  without  full  explanation  of  the  limits 
of  their  use)  is  likely  to  lead  to  a  very  false  sense  ot 
security. 

To  some  readers  it  may  seem  unnecessary  to  raise 
difficulties  over  the  confusion  of  causes  of  fallacies  with 
'  fallacies  *  themselves ;  but  the  fact  is,  that  there  are 
few  kinds  of  confusion  that  are  really  more  difficult  to 
avoid.  The  name  'Fallacy'  is  commonly  used  in  at 
least  four  different  senses,  and  before  proceeding  further 
there  may  be  some  use  in  setting  these  out,  and  choosing 
one  of  them.     A  '  fallacy '  is  used  to  mean : — 

(1)  A  piece  of  false  reasoning,  in  the  narrower  sense ; 

either  an  invalid  '  immediate  inference,'  or  an 
invalid  syllogism ;  a  supposed  equivalent  form 
which  is  not  equivalent,  or  a  syllogism  that 
breaks  one  of  the  rules. 

(2)  A  piece  of  false  reasoning,  in  the  wider  sense ; 

whereby,  from  true  facts,  a  false  conclusion  is 
inferred. 

(3)  A  false  belief,  whether  due  to  correct  reasoning 

from  untrue  premisses  (reasons  or  sources),  or 
to  incorrect  reasoning  from  true  ones. 

(4)  Any  mental  confusion  whatever. 

Now,  clearly  there  is  no  guesswork  required  for 
saying  what  is  wrong  with  a  given  immediate  inference, 
or  syllogism,  expressed  in  full.     It  either  is  or  is  not 


Chap.  IV.]  INTRODUCTORY.  173 

a  case  of  '  undistributed  middle,' '  illicit  process/  and  so 
on.  But  since,  in  practice,  arguments  are  very  rarely  so 
expressed,  we  really  run  a  considerable  risk  in  accusing 
a  reasoner  of  falling  into  one  of  these  paralogisms.  If, 
for  example,  a  person  appears  to  be  using  an  undis- 
tributed middle  term  (as  when  he  argues  that  some  one 
who  '  rushes  in  where  angels  fear  to  tread,'  is  therefore 
a  fool),  the  error — if  error  there  be — may  really  be  due 
either  to  his  ignorance  of  syllogistic  needs,  or  to  his 
mistakenly  confusing  the  major  premiss  with  its  re- 
ciprocal ('  all  those  who  rush  in,  etc.,  are  fools '),  or  to  his 
mistakenly  believing  the  reciprocal  true ;  or,  again,  to 
some  confusion  as  to  the  exact  meaning  of  some  of  the 
separate  words  employed.  And  to  accuse  him  of  undis- 
tributed middle  is,  in  practice,  interpreted  as  judging 
that  it  was  the  first  of  these  four  causes  to  which  the 
error  may  be  definitely  traced.  That  which  is  a  fallacy 
in  the  second,  third,  or  fourth  senses  above  noticed  may 
be  no  fallacy  in  the  first  sense  ;  and  similarly  that  which 
is  a  fallacy  in  the  third  and  fourth  senses  may  escape 
being  so  in  the  first  and  second  ;  and  '  mental  confusion ' 
is  obviously  wider  than  any  of  the  other  meanings, 
covering  cases  which  they  would  allow  to  pass  untouched. 
Hence,  the  narrower  the  meaning  we  give  to  the  word, 
the  more  liable  we  become  to  the  danger  of  undertaking 
to  guess  at  the  cause  ;  and  on  this  account  it  seems 
better  to  interpret  '  Fallacy '  in  the  fourth  of  the  above 
senses. 

There  is  indeed   one  way  in  which  the  old  names, 
9 


174  FALLACIES.  HPabt  IL 

or  many  of  them,  may  be  preserved  with  real  advantage : 
and  that  is,  not  by  simply  deploring  the  difficult}"  of 
identification  and  then  thinking  no  more  about  the 
matter,  but  by  trying  to  understand  clearly  the  causes 
of  it.  So  far  as  we  can  obtain  the  law  of  the  difficulty, 
we  are  in  a  fair  way  towards  being  able  to  judge  in  the 
given  case  whether  and  how  far  identification  is  possible. 
It  is  therefore  on  this  account  that  I  would  draw 
attention  to  the  risk  of  failure  that  is  always  run,  for 
the  sake  of  speed,  in  attempting  to  find  at  once  the 
source  of  a  given  fallacy.  However  valuable  such  a 
practice  may  be  for  saving  time,  and  however  justified 
in  certain  cases,  we  must  admit  with  Mill  and  Whately 
that  there  are  many  other  cases  where  it  necessarily 
fails.  The  remedy  seems  to  lie,  first  in  recognising 
clearly  and  consistently  this  possibility  of  failure, 
secondly  in  trying  to  improve  our  process  of  guesswork, 
and  lastly  in  providing  some  surer  if  more  lengthy 
method  to  fall  back  upon  in  doubtful  or  disputed  cases, 
— wherever  the  matter  is  more  important  than  the  time. 
Such  a  method  Logic  really  furnishes, — that  of  the 
Reduction  to  absurdity,  *  or,  as  it  is  more  popularly  called, 
*  pushing  the  argument  home,'  a  method  not  by  any  means 
infallible,  but  free  at  least  from  the  danger  just  referred 
to.     Although  Language  remains  faulty  and  treacherous, 

*  This  is,  however,  to  be  distinguished  from  the  process  so-called  by 
Euclid,  -which  corresponds  to  the  ancient  "  ductio  'per  contradictoriam 
propositionem  sive  per  impossibile,"  by  which  the  moods  Baroko  and 
Bohardo  were  to  be  justified.  See  Aristotle :  Top.  viii.  14.  See  also 
p.  853  of  this  book. 


Chap.  IV.]  INTRODUCTORY.  175 

and  our  knowledge  of  Nature  incomplete,  yet  if  this 
method  be  fairly  and  cautiously  applied  we  thus  avoid 
at  least  the  too  common  error  of  dogmatically  misreading 
the  mental  processes  of  other  people. 

This,  then,  will  be  the  plan  adopted;  and  having 
already  recognised  the  fact  that  to  guess  at  the  source 
of  fallacy  necessarily  exposes  us  to  a  certain  risk  of 
failure,  the  next  point  is  to  inquire  what  can  be  done 
to  improve  the  methods  of  guesswork. 


CHAPTER  V. 
THE  EMPLOYMENT  OF  GUESSWORK. 

I.  General  and  Special  Sources  op  Fallacy. 

For  the  purpose  of  attempting  to  detect  Fallacy 
ofF-hand,  it  is  clear  that  some  classification  of  fallacies 
is  in  the  first  place  required :  we  must  be  able  to  give 
the  detected  fallacy  a  name.  And  the  most  obvious  and 
useful  principle  of  classification  appears  to  be  the 
attempt  to  distinguish  (1)  the  main  sources  of  danger 
to  argument  in  general,  and  (2)  the  special  dangers 
to  which  special  forms  of  argument  are  chiefly  liable. 
Some  such  principle,  not  perhaps  always  intentionally 
followed  however,  seems  in  fact  to  lie  at  the  root  of  most 
of  the  distinctions  which  have  been  made  by  logicians, 
and  equally  of  those  which  have  won  a  permanent 
place  in  popular  usage.  Thus  the  great  distinction 
made  by  Aristotle,  between  fallacies  in  dictione  and 
extra  dictionenn,  calls  attention  to  one  large  general 
source  of  Fallacy, — the  snares  of  language  ;  while  inside 
the  second  main  class  the  varieties  are  partly  common 
to  all  kinds  of  argument, — as  the  Fallacia  accidentia 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWOHK.  177 

(interpreted  widely),  the  Ignoratio  elenchi,  and  the 
Petitio  principiiy — partly  special  to  special  arguments, 
as  the  Fallacia  consequentis,  the  Non  causa  pro  causd, 
and  the  Fallacia  plurium  interrogationum.  So  again 
Mill's  division  into  a  priori  fallacies  and  those  of  'in- 
ference,' aims  apparently  at  marking  off  in  the  first 
place  a  large  source  of  error  common  to  all  forms  of 
argument,  while  under  the  second  head  the  same  function 
is  performed  again  by  the  class  called  *  fallacies  of  con- 
fusion,' the  remainder  of  the  second  class  being  divided 
according  to  the  special  forms  of  Inference,  namely 
Induction  and  Deduction.  And  when  we  look  at  the 
names  of  fallacies  which  are  widely  recognised  in  popular 
usage,  this  principle  of  classification  is  equally  noticeable, 
'  verbal  ambiguity,'  '  missing  the  point,'  and  *  begging  the 
question,'  having  come  respectively  from  *  in  didione,' 
*  Ignoratio  elenchi'  and  'Petitio  principii;'  and  such 
names  as  '  false  analogy,'  *  over-generalisation,'  '  over- 
looking alternatives,'  etc.,  referring  more  directly  to 
failures  in  special  kinds  of  argument. 

I  propose  then  to  make  some  use  of  this  principle 
of  classification.  In  face  of  the  difficulties  to  be  en- 
countered, a  certain  aid  towards  satisfactory  guesswork 
may  perhaps  be  given  by  examining  broadly  both  the 
chief  snares  common  to  argument  in  general,  and  also 
those  characteristic  of  the  special  forms  or  types  of  argu- 
ment. And  the  discussion  of  both  will,  I  hope,  be  of 
service  towards  appreciating  the  value  and  meaning  of 
the  method  for  reducing  to  absurdity. 


178  FALLACIES.  [Pabt  IL 


II.  A  List  of  General  Objections  to  any  Argument. 

Probably  if  any  one  already  accustomed  to  the  practice 
of  detecting  Fallacies,  but  yet  possessing  a  mind  un- 
burdened with  the  more  abstruse  logical  technicalities, 
were  asked  to  classify  all  possible  objections  to  arguments 
in  general,  the  division  made  would  be  somewhat  as 
follows: — 

1.  That  the  Reason  given  (or  the  objection)  is  beside 
the  point. 

2.  That  the  Reason  given  begs  the  question. 

3.  That  some  important  factor  has  been  overlooked  or 
forgotten. 

4.  That  if  the  argument  be  cogent,  some  absurdity 
(or  at  least  untruth)  must  also  be  believed. 

At  any  rate  such  a  classification  does  not  err  on  the 
side  of  too  great  depth  or  intricacy.  Can  it  be  made 
useful  for  our  present  purpose  ? 

A  note  must  be  carefully  registered,  in  the  first  place, 
that  this  division,  however  obvious  at  first  sight,  is 
purely  one  of  convenience,  not  otherwise  defensible.  In 
strictness  these  four,  if  not  quite  alternative  attacks, 
each  equally  capable  of  being  made  against  any  unsound 
argument,  are  at  least  to  a  very  great  extent  overlapping. 
It  will  be  seen  that  the  first  of  these  objections  corre- 
sponds roughly  to  the  charge  technically  known  as  Igno- 
ratio  elenchi  ;  the  second  to  Petitio  pnncipii  ;  the  third 
and  fourth  having  received  no  technical  names.    But  so 


Chap.  V.]         THE   EMPLOYMENT  OF  GUESSWORK.  179 

long  ago  as  Aristotle's  time  it  has  been  pointed  out  *  that 
every  case  of  Non  sequitur  may  in  one  sense  be  viewed  as 
Ignoratio  elenchi;  while  it  is  quite  clear  that  the  first 
and  second  of  the  above  heads  are,  strictly  speaking, 
cases  of  'Untruth  implied.'  If  the  Reason  is  beside 
the  point,  or  if  the  sufficiency  of  the  Reason  itself 
depends  on  the  Thesis  being  true,  it  is  clear  that  the 
Thesis  cannot  really  depend  upon  the  Reason  in  the 
manner  implied  in  every  argument.  As  regards  Petitio 
pHncipii  it  would,  no  doubt,  be  considered  rather  a 
straining  of  language,  were  we  to  claim  that  the  other 
heads  might  be  brought  under  it :  and  yet,  in  this  rather 
far-fetched  sense  the  name  Petitio  princiini  is  some- 
times employed, — at  least  in  cases  where  the  point  is 
missed  and  in  those  in  which  some  palpable  absurdity 
is  implied.  For  when  we  give  as  valid  a  reason  which 
is  beside  the  actual  point  at  issue,  we  beg  (not  indeed  the 
expressed  original  question,  but)  a  question  then  perhaps 
for  the  first  time  seen  to  be  remotely  involved  in  it  and 
essential  to  its  establishment ;  namely,  that  of  the  con- 
nexion between  the  Thesis  which  is,  and  that  which  ought 
to  be  guaranteed.  This  may  be  seen,  for  example,  in  the 
case  where  metaphor  or  analogy  is  employed  in  argument : 
to  the  assertion  that  the  growing  size  of  London  bodes 
evil  to  England  because  London  is  the  heart  of  England, 
and  a  swollen  heart  is  a  sign  of  disease,  it  is  clearly 
optional  whether  we  object  that  "  R  is  beside  the  point, 
because  the  analogy  does  not  in  fact  apply"  or  that  " R 

*  Soph.  El.  vi. 


180  FALLACIES.  [Part  IL 

begs  the  question  how  far  the  analogy  holds  good,  which 
is  the  real  turning-point  of  the  argument;"  or,  again, 
that  R  and  T  together  imply  the  absurdity  (or  untruth)  of 
supposing  what  is  in  fact  a  mere  metaphor  to  hear  literal 
interpretation.  In  all  three  cases  the  objection  is  funda- 
mentally the  same,  and  our  adoption  of  one  form  or 
another  depends  solely  on  rhetorical  considerations. 
Again,  where  a  Reason  is  given  which,  taken  together 
with  the  Thesis,  leads  to  absurdity  or  untruth,  we  some- 
times hear  the  objection  brought  that  such  Reason  begs 
the  question  by  assuming  the  fact  on  which  the  question 
is  plainly  seen  to  turn.  As  De  Morgan  says  (Foi^mal 
Logic,  255),  though  he  strongly  objects  to  the  nomencla- 
ture— "It  is  the  habit  of  many  to  treat  an  advanced 
proposition  as  a  begging  of  the  question  the  moment  they 
see  that  if  established  it  would  establish  the  question." 
R  is  accused  of  covertly  assuming  the  truth  of  some  highly 
doubtful  proposition  which  is  plainly  required  to  establish 
T.  So  again  it  is  open  to  us  to  view  any  case  of  palpable 
question-begging  as  'beside  the  point,'  inasmuch  as  it 
provides  no  real  evidence  in  support  of  the  point  actually 
in  question.  If  for  the  Thesis  '  War  is  unjustifiable '  the 
Reason  be  given  '  We  ought  not  to  do  evil  that  good  may 
come,*  it  is  quite  optional  to  object,  either  that  '  this  begs 
the  question  whether  war  is,  on  the  whole,  an  evil,*  or  that 
'  the  maxim  is  an  excellent  one  in  itself,  but  beside  the 
point  in  the  present  case,  since  war  is  not  necessarily  a 
doing  of  evil'  *  And  lastly  it  does  not  need  any  lengthy 
*  Readers  who  have  been  interested  in  the  formerly  disputed  qaestion 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  181 

exposition  to  show  that  in  all  cases  where  Fallacy  has 
crept  into  an  argument,  some  relevant  fact,  whether  as  to 
things  or  as  to  the  meaning  of  names,  has  been  over- 
looked. "  "We  might,  perhaps,"  says  Mr.  Sully,*  "  charac- 
terize all  illusion  as  partial  view,"  and  elsewhere  he 
identifies  illusion,  at  bottom,  with  fallacious  inference. 

In  spite  of  such  difficulties,  however,  this  fourfold 
division  may  be  put  to  considerable  use  in  guessing 
at  the  seat  of  Fallacy.     But  it  will  need  some  special 

whether  or  no  the  Syllogism  itself  is  a  Petitio  principii,  will  easily  see 
the  connexion  of  what  has  just  been  said,  with  that  ancient  difficulty. 
Every  Syllogism  runs  a  risk  of  being  in  fact  a  Petitio  principii ;  it  is 
BO  unless  the  argument  employing  it  either  appeals  to  admissions  already 
made  (thus  becoming  a  legitimate  argumentum  ad  hominem),  or  else  only 
aims  at  forcing  into  explicitness  a  principle,  or  an  application  of  a 
principle,  on  which  the  point  at  issue  turns, — in  order  that  the  material 
truth,  as  yet  supposed  capable  of  disbelief,  of  such  principle  or  appli- 
cation may  be  now  inquired  into.  If  I  argue  that  A  is  B  because  A  is 
C  (or  because  C  is  B),  the  Syllogism  employed  is,  of  course — C  is  B: 
A  is  C  :  .'.A  is  B.  In  using  this  Syllogism  I  may  be  either  appealing  to 
a  former  admission  that  C  is  B  (or  that  A  is  C),  or  I  may  wish  now  to 
obtain  that  admission,  and  then  the  further  consequence  that  my  thesis 
is  true;  and  lastly  I  may  either  try,  consciously  or  unconsciously, 
to  hide,  or  may  openly  confess,  this  wish.  Supposing  the  Beason  itself 
true,  the  whole  question  of  the  truth  of  the  Thesis  turns  upon  the  truth 
of  such  further  assertion  implied  by  Eeason  and  Thesis  together,  and 
to  '  assume '  the  truth  of  such  further  assertion  is,  no  doubt,  to  '  assume ' 
that  upon  which  the  question  really  turns.  But  there  are  two  kinds  of 
assumption — underhand  (or  unconscious),  and  open, — and  it  is  only  the 
former  which  can  do  harm.  A  Syllogism  rightly  employed  is  just  as  much, 
and  no  more,  an  assumption  of  the  point  in  question  as  every  express 
assertion  is.  If  I  assert  that  A  is  B,  I '  calmly  assume '  that  such  assertion 
is  true ;  but  I  do  so  in  a  manner  which,  if  my  assumption  is  not  sup- 
ported by  an  appeal  to  valid  reasons,  exposes  me  at  once  to  the  necessary- 
hostile  criticism.  If  the  view  here  taken  of  the  burden  of  proof  be  a 
correct  one,  it  is  only  covert  assumptions  which  are  illegitimate. 
•  nhisions,  2nd  ed.  p.  836. 


182  FALLACIES.  [Part  IL 

care  in  keeping  the  classes  distinct.  We  shall  have  to 
limit  the  meaning  of  some  of  the  names,  in  a  way  which 
their  etymology  at  least  would  hardly  warrant. 


III.  The  Objection  Ignoratio  Elenchl 

First,  it  should  be  noticed  that  the  common  application 
of  the  terms  Ignoratio  elenchi  and  Petitio  principii 
is  rather  uncertain.  As  regards  the  former,  we  have 
already  seen  that  in  one  sense  it  may  be  stretched  to 
cover  nearly  every  possible  fallacy,  while  in  another  sense 
it  is  often  narrowed  to  misinterpretation  of  the  meaning 
of  the  Thesis.  A  third  sense,  rather  wider  than  this 
last,  is  simply  the  objection  that  owing  to  some  con- 
fusion or  other  as  to  meaning,  the  Reason  is  accepted  as 
a  guarantee  for  the  Thesis,  when  in  fact  either  this  actual 
Reason  at  most  guarantees  some  other  proposition  merely 
resembling  the  The&is  and  mistaken  for  it,  or  when  some 
other  proposition  merely  resembling  R  guarantees  this 
actual  Thesis.  When  the  charge  'R  beside  the  point' 
is  brought,  in  the  sense  here  referred  to,  what  is  meant 
is  that  owing  to  some  misunderstanding,  whether  of  R 
or  of  T,  the  former  is  unduly  accepted  as  a  guarantee 
for  the  latter.  To  use  an  expression  of  Mr.  Milnes' — 
"  The  journey  has  been  safely  performed,  only  we  have 
got  into  the  wrong  train." 

If  we  accept  this  meaning,  the  next  thing  is  to  dis- 
tinguish carefully  two  cases  of  misunderstanding;  first 
where,  without  any  opponent  as  yet  in  existence,  an 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWOKK.  183 

assertor  brings  forward,  in  support  of  his  Thesis,  some 
Reason  which,  though  really  valid  for  some  other  (similar) 
Thesis,  is  strictly  irrelevant  to  the  present  purpose  ;  and, 
secondly,  where  the  misunderstanding  takes  the  form  of 
an  objection  by  an  opponent,  to  an  assertion  made,  or 
an  argument  employed,  by  ourselves.  It  is  in  the  former 
of  these  two  cases  that  the  chief  practical  difficulty  is  to  be 
found,  but  in  both  cases  the  difficulty  is  considerable. 

In  no  department  of  logical  practice,  perhaps,  is  the 
danger  of  undue  dogmatism  so  great  as  in  that  of  deciding 
whether  misinterpretation  has  really  taken  place.  This 
is,  in  fact,  the  chief  point  at  which  the  functions  of  Logic 
are  apt  to  be  confused  with  those  of  Grammar.  Since  in 
any  advanced  language  there  is  much  substantial  agree- 
ment both  as  to  the  meaning  of  names  and  of  forms  of 
speech,  and  since  in  such  languages  Grammar  is  always 
at  hand  to  confirm  and  to  generalise  this  agreement  as 
far  as  possible,  there  springs  up  easily  the  supposition 
that  meaning  resides  solely  m  the  words  and  their 
arrangement,  that  a  printed  sentence  bears  its  full  inter- 
pretation on  its  face,  which  has  only  to  be  deciphered 
and  the  thing  is  done.  But,  as  a  fact,  interpretation  is 
far  from  being  so  simple  a  matter :  the  same  meaning 
may  be  expressed  in  many  different  forms,  and  the  same 
word  or  set  of  words  may  carry  many  different  shades 
of  meaning.  If  any  doubt  be  felt  on  this  head,  let  the 
reader  take  any  collection  of  ordinary  examples  of  pro- 
position, e.g.  those  in  chaps,  iil  and  iv.  of  Jevona' 
Studies  in  Deductive  Logic  (and  these,  be  it  rem«m- 


184l  FALLACIES.  [Pabt  IL 

bered,  are  always  artificially  straightforward),  and  ask 
himself  in  how  many  of  the  four  traditional  forms 
(A,  E,  I,  and  O),  each  will  bear  interpreting.  Still  .more 
uncertain  is  the  meaning  of  the  separate  names  em- 
ployed. A  few  there  are,  as  already  noted,  the  sense 
of  which  is,  practically,  fixed ;  but  these  are  com- 
paratively few.  Not  only  does  the  meaning  of  most 
words  in  common  use  undergo  a  constant  gradual  change 
as  time  goes  on,  but  at  the  same  period  it  varies  greatly 
according  to  the  varying  knowledge,  or  even  the  passing 
emotions,  and  physical  states,  of  the  speaker ;  and  much 
of  what  every  one  '  knows '  he  is  liable  to  forget.  All 
names  which  have  gathered  round  them  a  cluster  of 
inveterate  associations  (and  what  names  have  not  ?), 
depend  for  a  large  part  of  their  essential  meaning  on  the 
past  experience,  and  present  mental  states  and  habits,  of 
the  person  using  or  hearing  them.  Many  words  bore  a 
different  sense  to  ourselves  as  children  from  that  which 
they  bring  to  us  later  in  life :  though  the  old  names  and 
phrases  may  remain,  their  meanings  grow  and  alter  widely. 
So  again,  a  slight  difference  in  the  context,  or  even  in 
less  obviously  connected  circumstances,  will  often  make 
a  difference  of  meaning  amounting  to  the  actual  reverse 
of  that  conveyed  by  the  same  words  at  another  time : 
witness  the  possibility  of  "  damning  with  faint  praise," 
or  the  wrath  of  authors  whose  sentences  have  been 
criticised  apart  from  their  surrounding  explanations. 
We  need  not  search  further  for  illustrations  of  so  trite  a 
fact.     The  purpose  of  these  remarks  is  merely  to  bring 


Chap.  V.]        THE  EMPLOYMENT  OP  GUESSWORK.  185 

to  mind  the  many-sided  difficulties  attending  all  attempts 
at  finding  the  exact  meaning  of  an  assertion. 

To  all  this  it  may,  however,  be  answered  that,  just  as 
in  deciding  whether  a  proposition  is  real  or  not,  so  in 
deciding  the  total  question  of  its  meaning,  the  only 
feasible  plan,  where  doubt  exists,  is  to  put  questions 
until  such  doubt  is  removed.  It  is  here,  in  fact,  that  the 
practical  value  of  the  third  *  Law  of  Thought ' — that  of 
Excluded  Middle — comes  into  operation.  That  Law, 
regarded  as  a  statement  of  fact,  is  of  course  the  barest 
truism, — A  is  either  B  or  not-B:  everything  is  either 
something,  or  something  else.  But  its  value,  in  this 
connexion,  springs  from  the  fact  that,  having  postulated 
this  undeniable  truth,  we  gain  the  right  *  to  require  from 
a  speaker  the  answer  Yes  or  No  to  any  intelligible 
question  t  put  about  the  meaning  of  a  name  or  other 
form  of  speech.  "  When  you  say  that  Solomon  was 
wise,  do  you  mean  wise  according  to  our  present  standard, 
or  some  other  ? "  "  When  you  say  that  familiarity  breeds 
contempt,  do  you  mean  that  in  every  case  the  maxim 

•  It  is  very  difficult  to  avoid  neiTig  expressions  which,  strictly  inter- 
preted, may  seem  to  refer  to  some  set  of  artificial  rules  for  debate.  It 
is,  however,  possible,  I  hope,  to  keep  these  convenient  expressions,  and 
yet  strain  all  such  meaning  out  of  them  ;  using  them  only  for  brevity. 
Strictly,  of  course,  we  have  no  '  right  to  require '  any  answer  at  all : 
what  is  meant  is  only  that  if  no  answer  is  forthcoming,  the  argument 
falls  through,  since  either  the  Thesis  or  the  Reason  remains  *  unreal'  to 
«s  who  ask  the  question. 

t  It  should  be  noticed  that  if  A  sometimes  means  B,  and  sometimes 
not,  the  question,  "  Do  you  mean  A  or  not  ? "  bec-omes  no  longer  in. 
telligible. 


186  FALLACIES.  [Part  IL 

holds  true  ? "  "  When  you  say  that  some  Irish  are  indus- 
trious, do  you  mean  that  the  majority  are  idle  ? "  When 
an  hon.  member  said  that  the  House  of  Commons  is 
'  largely  composed  of  English  gentlemen,'  did  he  mean  to 
imply  that  it  is  not  entirely  so  composed  ?  There  is  no 
limit  to  the  possible  varieties  of  question  that  might  be 
put,  and  wherever  the  question  itself  is  intelligible,  only 
the  two  answers — ^Yes  or  No — are  possible,  and  one  or 
the  other  must  be  true.  Where  doubt  arises  as  to 
meaning,  therefore,  we  have  this  method  at  hand  for 
removing  it. 

But  the  chief  source  of  misinterpretation  is  the  fact 
that  such  doubt  does  not  arise  as  freely  as  could  be 
desired.  We  do  not  habitually  weigh  either  our  own 
assertions  or  those  of  other  people — life  being  short,  and 
occupations  various, — but  are  content  to  throw  our  words 
out  somewhere  near  the  mark,  and  to  seize  the  gist  of 
what  is  said ;  glad  if  we  escape  the  grosser  kinds  of  in- 
accuracy. Very  likely  there  are  excellent  reasons  for  this 
practice,  but  it  has  its  dangers  also ;  and  it  is  about  the 
dangers  only  that  we  are  here  inquiring.  Apart  from 
the  plan  of  systematic  questioning,  can  anything  be  done 
to  avoid  misinterpretation  ? 

Much  may  be  done,  no  doubt,  but  not  in  the  shape  of 
a  few  plain  rules.  To  deal  with  the  pitfalls  of  language 
at  all  fully,  at  least  a  separate  volume  would  be  required. 
In  one  sense,  indeed,  the  subject  is  inexhaustible.  No 
one  can  pretend  to  be  perfectly  safe  from  all  danger  of 
misinterpreting  language  until  he  can  claim  a  complete 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  187 

knowledge  of  all  nameable  things,  and  also  entire  freedom 
from  all  effects  of  our  ancestors'  mistakes  in  naming ; 
and,  so  far  as  this  goal  remains  at  present  unattained,  so 
far  there  exists  a  source  of  misinterpretation  against 
which  nothing  can  securely  guard.  It  is  true,  no  doubt, 
that  there  are  many  errors  in  interpretation  which 
spring,  at  least  directly,  not  from  imperfect  acquaint- 
ance with  the  things  that  bear  the  names,  but  from 
ignorance  of  the  principles  of  naming,  classifying,  and 
defining,  from  too  careless  employment  of  language,  or 
from  too  ready  subservience  to  its  tyranny.  But  the 
task  of  completely  remedying  even  these  defects  is  a 
somewhat  more  extensive  one  than  can  be  here  at- 
tempted, except  by  means  of  occasional  and  indirect 
suggestions. 

It  is  obvious,  further,  that  if  there  is  to  be  an  abso- 
lutely clear  mutual  understanding  between  speaker  and 
audience  as  to  the  meaning  of  every  separate  word  em- 
ployed, and  also  of  the  assertion  as  a  whole,  a  larger  part 
of  every  speaker's  life  would  be  occupied  in  the  process 
of  defining,  or  explaining  his  statements,  than  could  well 
be  spared  from  his  other  occupations ;  and  that,  long 
before  the  meaning  of  most  assertions  could  be  settled, 
their  value  as  practical  information  would  have  passed 
away.  Accordingly,  the  point  of  first  importance  for 
practice  is  to  know  on  what  principles  the  compromise 
had  better  be  conducted ;  when  once  there  is  seen  to  be 
need  of  inquiry  into  the  special  meaning  given  to  some 
word  or  phrase,  the  process  of  inquiry  is  simple  enough. 


188  FALLACIES.  [Pabt  H. 

and  has  been  already  sufficiently  indicated.  To  a  de- 
finite question  a  definite  answer  may  be,  with  reason, 
demanded. 

Where  there  are  already  two  opponents,  though  Igno- 
ratlo  elenchi  is  unfortunately  common  enough,  it  is  far 
less  dangerous  than  in  the  other  case.  As  a  rule,  when 
we  are  met  by  opposition  we  are  ready  enough  to 
discover  any  misunderstanding  of  our  views.  The  grosser 
cases,  at  least,  therefore,  would  present  no  difficulty :  it 
will  be  sufficient  to  call  to  mind  a  few  of  the  leading 
varieties.  Thus,  mildly  denying  that  a  certain  thing  is 
absolutely  all-important,  we  are  met  by  arguments  to 
show  that  it  hes  some  use:  boldly  pointing  out  that 
something  else  is  altogether  valueless,  we  are  met  by  the 
answer  that  we  '  can't  expect  perfection  : '  asserting  that 
some  doctrine  lacks  arguments  to  prove  its  truth,  we  are 
referred  to  excellent  reasons  for  believing  in  its  utility  : 
endeavouring  to  trace  the  manner  in  which  some  highly 
developed  growth  (e.g.  conscience)  originated,  we  are 
supposed  to  be  refuted  by  a  mere  description  of  its 
present  nature :  disputing  an  argument,  or  an  instance, 
we  are  supposed  flatly  to  deny  the  theory  in  support 
of  which  these  were  brought  forward :  making  some 
merely  tentative  suggestion  we  are  asked  for  definite 
proofs.  The  varieties  are  endless,  and  the  reader's  ex- 
perience will  easily  supply  him  with  a  longer  list  of 
instances  than  we  need  here  set  out. 

But  the  real  importance  attaching  to  this  kind  of 
Ignoratio  elenchi  begins  when  we  reach  the  finer  shades 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  189 

of  it  There  is  no  doubt  that  the  most  frequent  cause 
both  of  real  misunderstanding  and  also  of  interpretation 
which  is  only  too  penetrating,  is  the  attempt  to  read 
between  the  lines  of  what  is  said.  Time  being  short,  it 
seems  to  be  generally  recognised  that  some  ellipsis  in 
expression  may  as  a  rule  be  expected.  It  saves  time  and 
trouble  in  many  cases  to  go  behind  the  actual  words, 
answering  not  what  they  strictly  say,  but  what  the 
objector  supposes  they  really  intend  to  insinuate.  There 
are  familiar  euphemisms,  for  instance,  whose  ironical 
meaning  is  hallowed  by  custom ;  and  there  are  ways  of 
saying  much  by  saying  little, — and  vice  versd. 

But  probably  the  most  dangerous  of  all  the  sources  of 
misunderstanding,  is  the  gradual  change  that  unavoidably 
takes  place  in  the  accepted  meaning  of  words,  so  that 
both  old  and  new  meanings  are,  for  a  time  at  least,  left 
existing  side  by  side.  The  most  marked  examples  of  this 
are  perhaps  those  due  to  the  influence  wrought  on  lan- 
guage by  Science,  or  the  deepening  of  knowledge,  on  the 
one  hand,  and  by  the  allegorical  or  superficial  spirit  on 
the  other  ;  very  many  words  possess  in  this  way  no  less 
than  three  broadly  marked  meanings, — the  scientific  (or 
technical),  the  popular,  and  the  poetical.  The  various 
meanings  in  which  the  familiar  word  '  Law '  is  used,  will 
perhaps  sufficiently  illustrate  what  is  here  intended.  Or 
again,  through  what  is  loosely  called  mere  lapse  of  time, 
the  meaning  of  a  word  may  wholly  alter;  as  the  word 
'  Sophist,'  originally  from  aotpog,  has  now  come  to  mean 
a  quibbler.     A  public  instance  of  Ignoratio  elenehi  due 


190  FALLACIES.  CPabt  IL 

to  this  latter  cause,  was  presented  in  a  recent  trial,*  "  It 
was  complained,"  said  counsel,  "  he  had  written  '  I  never 
expected  to  hear  a  coxcomb  ask  two  hundred  guineas  for 
flinging  a  pot  of  paint  in  the  public's  face,'  but  .... 
what  is  a  '  coxcomb '  ?  /  have  looked  out  for  the  word  and 
find  that  it  comes  from  the  old  idea  of  the  licensed 
jester,  who  wore  a  cap  and  bells  with  a  cock's  comb  in  it. 
If  that  is  the  true  definition,  Mr.  Whistler  should  not 
complain."  So  in,  perhaps,  the  majority  of  cases  where 
Etymology  is  relied  upon  by  an  afterthought  as  giving 
the  '  true  '  meaning  of  a  word  at  the  present  day,  there 
is  involved  some  attempt  to  use  the  word  in  one  meaning 
and  to  defend  it  in  the  other.f 

We  have  already  had  occasion  to  notice  George  Eliot's 
reference  to  "  those  undeniable  general  propositions  which 
are  usually  intended  to  convey  a  meaning  very  far  from 
undeniable,"  and  it  is  not  only  general  propositions  but 
gejieral  names  also  that  are  used  largely  in  this  manner. 
The  meaning  of  any  name  consisting,  as  it  does,  of  very 
many  particular  facts  regarding  the  objects  named,  it 
becomes  easy  on  occasion  to  forget  conveniently  some  of 
these  facts  while  defending  our  use  of  the  word,  although 
we  were  far  from  forgetting  them  in  the  meaning  really 

*   Wliistler  v.  RusTcin. 

t  Cf.  Geo.  Bentham,  Outline  of  a  New  System  of  Logic.  "  Where 
correct  information,  and  consequently  perspicuity  in  language  is  the 
object,  the  greatest  attention  should  be  paid  to  employ,  in  preference  to 
others,  such  figures  as  have  by  long  use  lost,  as  it  were,  their  original 
sense."  Cf.  also  H.  Spencer,  Psychology,  vol.  i.  p.  97.  "  The  best  words 
are  those  from  which  long  use  has  worn  away  all,  or  nearly  all,  traces 
of  their  origin." 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  191 

intended  to  be  conveyed.  The  gathered  associations,  for 
instance,  which  words  take  on,  and  which  they  are  sure 
to  convey  when  used,  can  be  very  easily  left  out  of  sight 
while  defending  our  use  of  them.  This  is  especially 
insidious  in  the  case  where  the  meaning  of  the  word  used 
is  relative  to  some  standard,  and  where  truth  or  false- 
hood depends  upon  the  standard  taken.  As  marked 
instances  may  be  mentioned  'good'  and  'bad,'  'great' 
and  'small,'  '  hot '  and  '  cold,'  and  all  names  which  con- 
fessedly indicate  points  variably  selected  on  a  scale.  In 
its  finer  shades  the  danger  is  almost  ineradicable,  since 
the  standard  employed  by  different  people  in  judging 
is  apt  to  vary  with  their  personal  peculiarities,  tem- 
porary or  habitual,  and  past  experience ;  so  that  where 
no  thermometer  can  be  appealed  to  it  becomes  exceed- 
ingly difficult  to  fix  any  objective  standard  at  alL  Even 
if  we  understand  our  intimate  friends,  it  is  notoriously 
difficult  to  make  full  allowance  for  difference  of  standard 
in  the  case  of  all  our  casual  acquaintances. 

It  is  easy,  however,  in  this  manner  to  enumerate  a 
few  of  the  leading  ways  in  which  assertions  may  be  mis- 
understood, and  even  to  write  a  loose  and  general  homily 
upon  human  liability  to  error  in  this  respect.  But  there 
seems  to  me  very  little  practical  value  in  so  doing.  The 
practical  question  would  be, — What  is  it  incumbent  on  us 
to  do,  for  the  purpose  of  detecting,  and  so  avoiding, 
misinterpretation?  And  to  answer  this  with  any  real 
completeness  would  lead  us  further  afield  than  we  can 
here  afford  to  go. 


192  FALLACIES.  [Pabt  IL 

But  as  regards  the  first  of  the  two  kinds  of  misunder- 
standing, it  may  perhaps  be  suggested  as  a  broad  general 
rule  that  inquiry  into  meaning,  for  the  purpose  of  raising 
the  objection  that  II  is  beside  the  point,  is  only  advisable 
where  the  person  inquiring  has  himself  a  definite  view, 
if  not  of  all  the  possible  ambiguities  involved,  at  least  of 
the  fact  that  some  given  ambiguity  is  probable.  It  is 
true  that  in  this  way  much  false  argument  would,  pass 
unnoticed,  but  the  only  alternative  seems  to  be  a  loss  of 
more  time  than  the  results  would  probably  justify.  If 
in  every  case  where  an  assertion  is  made  and  grounded, 
it  were  to  become  at  once  incumbent  on  us  simply  to 
assume,  until  the  contrary  was  shown,  that  some  irrele- 
vance was  present  between  R  and  T,  it  is  clear  that  the 
waste  of  time  would  be  on  the  whole  enormous. 
Although  Ignoratio  elenchi  may  be  the  commonest  of 
all  fallacies,  and  although,  perhaps,  some  slight  shade 
of  uncertainty  as  to  our  meaning  is  present  in  nearly  all 
assertions  actually  made,  nothing  would,  I  think,  be 
practically  gained  by  treating  intelligent  assertion  as  the 
exception,  verbal  confusion  as  the  rule.  There  should  be 
something  to  set  us  on  the  track  of  an  Ignoratio  elenchi; 
we  should  not  be  left  under  the  necessity  of  inquiring 
for  it  at  large. 

If  this  be  admitted, — and  I  see  no  resource  but  to 
make  the  admission, — it  follows  that  the  power  of  guard- 
ino-  asrainst  this  kind  of  mental  confusion  is  not  one 
which  can  be  given  in  a  few  hours  or  days,  by  the 
careful  study  of  any  dissertation  on  the  subject,  however 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  193 

searching  and  complete.  It  must  be  rather  a  growth, 
dependent  on  the  growing  power  and  habit  of  distinguish- 
ing between  the  different  senses  which  any  given  word 
or  phrase  may  bear.  It  is  the  power  of  seeing  difference 
that  is  of  prime  importance, — difference,  in  this  case, 
between  one  possible  meaning  and  another.  And  the 
power  of  seeing  differences  cannot  be  obtained  by  merely 
recognising  its  value,  though  that  is  no  doubt  one  im- 
portant step  towards  the  attainment  of  the  power. 

As  regards  the  second  kind — that  which  more  truly 
corresponds  to  the  literal  meaning  of  Ignoratio  elenchi, 
— it  may  also,  I  think,  be  laid  down  that  the  assertor 
is,  in  every  case,  the  arbiter  of  what  he  means  to  say. 
Where,  under  cross-examination,  he  contradicts  himself, 
or  shifts  his  ground,  this  can  be  pointed  out,  and  the 
request  can  be  made  that  he  will  abide  by  one  alterna- 
tive or  the  other.  He  either  means  a  given  thing  or  he 
does  not.  There  is  no  middle  ground  between  '  Yes '  and 
'No/ 


IV.  The  Objection  Pjetitio  Pbincipii. 

A  similar  difficulty  exists  in  fixing  the  meaning  of 
Petitio  principii,  to  that  noticed  already  in  the  case 
of  Ignoratio  elenchi.  De  Morgan  observes  *  that 
"Aristotle  hardly  ever  uses  the  phrase  apxnv  aiTHirOai, 
pHncipium  petere :  it  is  To  iK  apxvQ,  and  To  Iv  apxg, 
that  which  is  (ought  to  come)  out  of,  or  is  in,  the  prin- 

•  Formal  Logic :  p.  256. 


194  FALLACIES.  [Past  II. 

cipla     By  the  word  principium  he  distinctly  means  that 
which  can  be  knoum  of  itself."  ..."  Among  the  earlier 
modem  writers,  as  far  as  I  have  seen  them,  there  is  some 
diversity  in  their  description  of  the  petitio  priTidpii. 
That  the  priTieipium  was  meant  to  be  the  thing  known 
of  itself,  the  apxn  of  Aristotle,  as  far  as  the  introduction 
of  the  word  is  concerned,  seems  clear  enough.     Was  it 
not  then  by  a  mere  corruption  that  it  was  frequently 
confounded  with  the  conclusion,  the  '  quod  in  principio 
quoesitum  fuit?'    Did  not  the  same  inaccuracy,  which 
confounds  the  To  £v  «/ox5  ^^  Aristotle   with  the   apxri 
itself,  govern  the  change   of  the   word  ?     Most  writers 
.  take  the  fallacy  of  the  petitio  prindpii  as  meaning  that 
in  which  the  conclusion  is  deduced  either  from  itself, 
or  from  something  which   requires   proof  more,   or  at 
least  as  much,  ignotius,  aut  seque  ignotum"    And  De 
Morgan's  own  opinion  seems  to  be  {ibid.  p.  254),  that 
"  strictly  speaking,  there  is  no  formal  petitio  principii 
except  when  the  very  proposition  to  be  proved,  and  not 
a  mere  synonym  of  it,  is  assumed."     Nothing,  however, 
appears  to  be  really  gained  by  restricting  the  name  to 
,so  small  a  compass  as  this ;  and  there  is  no  doubt  that 
such  a  restriction  would  be  very  much  at  variance  with 
the  popular  acceptation  of  the  term.     Still,  some  restric- 
tion seems  needed,  or  else,   if  we  define  it  as  'covert 
assumption '  in  general,  it  is  difficult  to  say  where  the 
application  would  really  stop.     Although,   even  on  so 
wide  a  view,  deductive  proof  would  not  be  a  begging  of 
the  question,  since  there  the  turning-points  of  the  argu- 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  195 

ment  are  openly  appealed  to ;  yet,  on  the  other  hand,  we 
should  have  to  say  that  question-begging  in  its  finer 
shades  begins  where  there  is  even  an  unconscious  fear 
of  allowing  Principle  and  Application  to  stand  their 
trial. 

Question-begging,  then,  as  we  shall  understand  the 
term,  never  arises  except  in  two  cases ;  namely,  (1)  where 
the  relevancy,  and  (2)  where  the  truth  of  R  is  already 
called  in  question,  and  where  in  answer  to  such  objection, 
some  proposition  equivalent  to  (or  including)  the  original 
T  is  given  in  support.  Of  the  first  of  these  cases,  an 
example  given  above  (p.  169)  may  be  taken  as  fairly 
typical, — "  Every  effect  must  have  a  cause  (T),  since 
otherwise  it  would  not  be  an  effect  (R)."  We  have  seen 
that  to  call  in  question  the  relevancy  of  the  Reason  is,  in 
other  words,  to  ask  for  the  missing  premiss  required  for 
full  Demonstration,  and  here  it  is  plain  that  this  can  only 
be  the  original  Thesis  itself — "  Every  effect  must  have  a 
cause."  For  if  it  be  possible  that  an  '  effect '  should  hap- 
pen without  a  cause,  then  the  special  signification  which 
the  name  '  effect '  is  employed  to  bear  would  be  lost,  and 
its  value  as  a  label  would  accordingly  be  spoilt.  Hence 
in  order  to  complete  the  formal  cogency  of  the  argument, 
we  need  the  material  truth  of  the  Thesis, — which  is  just 
the  point  at  issue.  For  the  second  case  we  may  take  as 
a  conspicuous  example  the  dialogue  given  by  Whately  in 
illustration, — but  somewhat  altered  and  shortened : — 

"  '  Every  particle  of  matter  gravitates  equally.'  [T]. 
'  Why  ? ' 


196  FALLACIES.  [Paet  IL 

*  Because  those  bodies  which  are  heavier  always  contain  more  par- 
ticles, even  if  more  closely  condensed.'     [R]. 

'  How  do  you  know  that  ? '  [i.e.  '  I  doubt  whether  R  is  true.''} 
'  Because,  all  particles  of  matter  gravitating  equally,  [original  TJ 
that  mass  which  is  speciBcally  the  heavier  must  needs  have  the  more 
of  them  in  the  same  space.' " 

It  is  seldom,  of  course,  in  practice  that  we  find  Petitio 
principii  thus  openly  relied  upon.  Actual  arguments  are 
usually  longer,  more  complex,  and  less  explicit,  than 
those  which  are  required  for  illustration.  As  Whately 
puts  it,  "  A  very  long  discussion  is  one  of  the  most 
effectual  veils  of  Fallacy.  Sophistry,  like  poison,  is  at 
once  detected  and  nauseated  when  presented  to  us  in  a 
concentrated  form ;  but  a  Fallacy  which  when  stated 
barely,  in  a  few  sentences,  would  not  deceive  a  child,  may 
deceive  half  the  world  if  diluted  in  a  quarto  volume." 
But  it  is  by  seeing  any  fallacy  in  its  nakedness  that 
we  can  best  learn  its  central  nature,  and  hence  the  need 
of  sometimes  appealing  to  examples  which  are  so  obvious 
as  to  be  free  from  serious  harm.  The  real  diflficulty,  for 
practice,  always  lies  in  the  stripping  off  disguises,  and 
reducing  what  is  said,  and  urged,  to  T  and  R 

And  here,  too,  when  we  raise  the  aU-important  ques- 
tion as  to  the  means  of  deciding  in  practice  whether 
question-begging  has  in  fact  taken  place,  we  become 
extremely  liable  to  the  danger  of  accusing  an  opponent 
unjustly ;  for  the  means  of  escape  are  numerous.  Take 
for  instance,  the  following  argument  of  Mr.  Jermyn  to 
Felix  Holt :  "  You  must  permit  me  to  check  your  use  of 
the  word  'bribery.'  The  essence  of  bribery  is  that  it 
should  be  legally  proved.     Unproved  bribery  does  not 


Chap.  V.]        THE  EMPLOYMENT  OF  GUESSWORK.  197 

exist."  Here  we  may,  perhaps,  have  a  very  strong 
suspicion  that  the  Thesis  is  needed  to  support  the 
Reason.  The  Thesis  evidently  is  "  This  case  >^  (i.e.  differs 
from)  bribery;"  and  the  Reason  "Bribery  — >  judicial 
conviction  thereof,"  (the  further  assertion  being 
"This  case  \  >  judicial  conviction  of  bribery.")  It 
seems  almost  quixotic  to  hesitate  to  accuse  the  speaker 
of  begging  the  question,  for  it  is  clear  that  if  this 
case  is  bribery  (which  is  the  point  at  issue')  the  Reason 
must  be  untrue,  —  provided,  at  least,  as  Felix  Holt 
would  certainly  have  admitted,  that  no  judicial  decision 
had  yet  been  given  against  the  case  in  question.  And 
yet,  if  we  accuse  Mr,  Jermyn  of  begging  the  question, 
he  has  an  easy  escape.  "I  mean,"  he  would  say,  "to 
assert  in  the  plainest  language,  that  it  is  little  short 
of  libellous  to  accuse  another  person  of  bribery  with- 
out bringing  legal  proof  to  support  such  accusation." 
This  may,  it  is  quite  evident,  have  been  his  real 
intention  in  the  speech.  That  is,  his  speech  may 
have  been  an  Ignoratio  elenchi  so  far  as  the  question 
bribery  or  no  bribery  is  concerned.  But  by  treating  the 
argument  in  a  less  hasty  manner,  the  covert  assumption 
may  be  prevented  quite  as  effectually  and  without  run- 
ning the  risk  of  mistaking  the  speaker's  intention.  "  Do 
I  understand  you  to  assert,"  we  might  ask,  "  that  if  A 
pays  B  for  his  vote,  no  bribery  bag  been  committed, 
unless  and  until  the  fact  is  proved  in  a  court  of  law  ?  If 
such  a  transaction  does  not  in  itself  deserve  the  name  of 

bribery,  what  name  does  it  deserve  exactly?    It  is  of 
10 


198  FALLACIES.  [Part  IL 

such  transactions  that  I  wish  to  speak,  whatever  their 
name  may  be." 

So  far  as  question-begging  may  be  due  to  misinter- 
pretation of  the  language  used,  the  difficulties  are  of 
course  the  same  as  those  briefly  noticed  in  the  preceding 
section.  But  more  commonly  it  is  the  result  of  much  the 
same  state  of  mind  as  that  which  leads  to  Platitude.  We 
have  already  had  occasion  to  notice  the  nature  of  the 
harm  done  by  tautologous  propositions  and  circular  ex- 
planations, and  since  Proof  is  the  counterpart  of  Explana- 
tion, and  every  argument  merely  a  complex  proposition, 
it  is  easy  to  see  the  fault  of  circular  Proof.  If  we  start 
with  the  implied  supposition  that  the  Thesis  is  true,  it  is 
obvious  that  the  more  correct  the  subsequent  logical 
process,  the  more  certain  shall  we  be  of  reaching  the 
required  result.  Such  Thesis  has  therefore  had  no  fair 
trial:  its  supposed  'proof  has  been  a  pretence.  Essen- 
tially the  same,  too,  is  that  commonest  and  most  insidious 
of  all  practices,  the  employment  of  what  Bentham  called 
"  question-begging  names."  If  a  name  properly  belongs 
to  S,  the  whole  meaning  of  that  name  is  applicable :  but, 
at  the  same  time,  if  ^art  of  the  meaning  is  plainly  ap- 
plicable, we  are  apt  to  suppose  that  the  name  may  be 
'  properly '  applied.  In  this  way  the  leap  from  part  to 
whole   is    easily    made,   and    the   assumption    hidden.* 

•  This  form  of  Petitio  principii  is  of  near  kindred  to  False  Analogy 
(see  p.  265),  and  also  to  material  nn truth  of  the  minor  premiss  in  an 
ordinary  deductive  argument.  The  difference  is,  in  fact,  like  that  be- 
tween analogy  and  metaphor,  a  gradual  difference,  depending  on  the 
degree  of  explicitness  merely.     In  the  deductive  argument  we  rest  our 


diiAP.  v.]        THE  EMPLOYMENT  OF  GUESSWOBK.  199 

It  is  not,  however,  only  when  we  wish  to  deceive,  nor 
even  only  when  we  use  words  carelessly,  that  this  danger 
arises :  for  the  number  of  words  that  have  gathered  no 
associations — especially  associations  of  praise  or  blame 
— is  comparatively  small,  and  with  the  best  intentions 
and  the  greatest  care  it  is  difficult  to  avoid  all  taint  of 
question-begging.  It  is  through  the  power  of  these 
associations  to  prejudge  a  question  that  so  much  import- 
ance is  attached  to  the  exact  name  given,  even  by  a  person 
who  is  himself  fully  capable  of  using  words  as  counters 
merely :  in  the  absence  of  a  colourless  word,  and  in  the 
presence  of  two  words  highly  tinged  with  opposite 
colours,  he  is  forced  to  choose  that  which  will  mislead 
the  least.  "  It  is  said  that  we  have  failed  in  Ireland. 
I  do  not  admit  the  failure.  I  admit  the  success  to  be  in- 
complete." In  the  same  way,  the  choice  between  '  reign- 
ing '  and  '  governing,'  between  '  sovereign '  and  '  suzerain,' 
between  '  mob-rule '  and  '  popular  government,'  between 
'  liberty !  and  '  license,'  between  '  famous '  and  '  notorious,' 
and  between  endless  other  pairs  of  alternatives,  may 
often  lead  to  unavoidable  unfairness,  or  at  best  to  a  rough 
balance  between  opposite  wrongs. 

The  remedy  is  essentially  the  same  in  this  case  as  in 
all  other  cases  of  Petitio  principii;  and,  in  a  wider 
sense,  in  all  cases  of  fallacy, — the  forcing  into  daylight 
that  which  would  prefer  obscurity.   Names  in  themselves 

case  quite  openly  on  the  disputable  premiss  that  '  S  is  M ; '  in  the  argu- 
ment from  analogy  we  suggest  '  S  is,  as  it  were,  M,'  or  '  practically  the 
same  as '  M ;  while,  if  we  desire  to  beg  the  question  by  means  of  a 
name,  we  assume  as  quietly  as  possible  that  the  name  applies. 


200  FALLACIES.  [Pabt  II. 

are  harmless  so  long  as  their  misleading  associations  can 
be  kept  away  from  them,  and  by  putting  the  point-blank 
question  whether  or  no  this  or  that  meaning  is  intended, 
the  assumption,  if  any,  may  be  compelled  to  produce  its 
credentials,  or  to  confess  that  these  are  wanting.  More 
than  this  Logic  can  never  do.  A  fallacy  stopped  at  one 
moment  may  always  bide  its  time,  and  come  into  opera- 
tion again  when  the  incident  has  been  forgotten  and  the 
pressure  removed:  and,  as  just  seen,  this  is  a  danger 
which  all  names  that  are  rich  in  gathered  associations 
especially  tend  to  foster.  On  this  account  it  is  that  in 
cases  where,  as  so  often  in  Politics,  the  determination  is 
strong  on  both  sides  to  take  every  possible  advantage, 
however  unfair,  there  is  often  practically  no  better  re- 
source, even  in  the  interests  of  truth  and  fairness,  than 
to  meet  question-begging  with  its  own  weapons,  just  as 
one  false  analogy  may  often  be  met  and  destroyed  by 
another  equal  and  opposite.  In  this  way,  out  of  two 
wrongs  a  rough  and  ready  right  may  be  made  to  emerge. 
But  here  we  certainly  step  over  the  line  which  divides 
Logic  from  Rhetoric,  or  the  task  of  detecting  and  recog- 
nizing Fallacy  (or,  as  an  alternative,  preventing  it  for 
the  moment)  from  the  wider  problem  of  counteracting  its 
operation- 


CHAPTER  VL 
THE   EMPLOYMENT  OF    GUESSWORK:   CONTINUED. 

I.  The  Objection  *A  Factor  overlooked.' 

It  is  difficult  to  find  any  one  short  name  which  shall 
fairly  describe  the  third  of  our  four  general  objections 
to  an  argument.  We  have  already  noticed  that  in  the 
ordinary  sense  of  the  words,  some  important  factor  has 
been  overlooked  or  forgotten  wherever  any  fallacy — even 
Ignoratio  elenchi  or  Petitio  principii — has  been  com- 
mitted ;  so  that  the  name  here  taken  is  too  vague  to  be 
really  descriptive.  And  the  same  difiiculty  seems  to 
attach  to  any  other  short  name  that  can  be  suggested ; 
thus  if,  for  example,  we  attempt  to  sum  up  this  third 
objection  as  the  charge  of  *  superficiality  of  view,'  it 
will  be  necessary  to  add  that  the  '  view '  spoken  of  may 
be  either  a  view  of  objects,  qualities,  and  events,  directly, 
or  a  view  of  the  meaning  of  names  and  propositions. 
For  sometimes,  in  proving,  we  make  use  of  knowledge 
already  formulated,  and  sometimes  we  go  direct  to  the 
facts  for  ourselves  :  while,  according  to  the  special  mode 
of  argument  employed,  will  be,  to  some  extent,  the  special 
liability  to  error. 


202  FALLACIES.  [Part  IL 

Without,  then,  spending  time  in  trying  to  get  a  per- 
fectly accurate  name  for  the  purpose,  it  becomes  necessary 
now  to  examine  briefly  at  least,  the  leading  types  or 
forms  of  argument,  noticing  the  points  at  which  they 
are  specially  vulnerable,  and  the  special  form  which  the 
objection  may  take.  And  in  spite  of  all  difficulties  and 
complications,  it  will  be  found  that  the  possibilities  of 
fallacy  are,  fundamentally,  fewer  and  simpler  than  might 
at  first  be  supposed.  Although  the  kind  of  argument 
employed  may  to  a  great  extent  be  used  as  the  key  in 
guessing  at  the  seat  of  possible  error,  yet  the  value  of 
the  key  will  be  much  increased  by  recognising  the 
essential  similarity  of  dangers  which  thus  take  on  some- 
what different  forms. 

IL  The  Types  of  Argument. 

§  1.  Introductory. 

In  reducing  the  almost  endless  variety  of  possible 
arguments  to  a  few  generalised  types,  it  must  be  remem- 
bered that  these  can  only  stand,  towards  the  arguments 
actually  found  in  use,  in  somewhat  the  same  relation  as 
the  '  roots '  of  language  are  (by  some)  supposed  to  stand 
towards  modern  forms  of  speech.  That  is  to  say,  the 
forms  of  argument  now  commonly  in  use  are,  for  the 
most  part,  much  more  complicated  than  these  types ;  and 
yet,  in  spite  of  all  their  complications,  they  are  capable 
of  analysis ;  the  roots,  however  modified  and  combined, 
can  stm  be  discovered  in  them. 


Chap.  VI.]       THE  EMPLOYMENT  OF   GUESSWORK.  203 

Without  some  such  artificial  simplification  of  the  in- 
quiry, it  would  be  practically  impossible  to  find  a  path 
at  all  securely  through  the  maze  of  details  presented ; 
and  with  due  precautions  there  need  be  no  more  danger 
in  this  expedient  than  in  an}'^  other  employment  of  the 
generalising  or  simplifying  process.  If,  as  is  frequent  in 
real  life,  a  given  argument  employs  in  combination 
several  of  these  typical  forms,  it  is  only  by  guarding 
against  the  dangers  to  which  each  part  of  the  complex 
whole  is  separately  liable,  that  we  can  take  the  whole 
in  hand.  Failing  some  method  of  the  kind,  we  should 
require  so  large  a  number  of  special  rules  of  evidence  that 
to  frame,  to  grasp,  or  to  handle  them  effectually  would 
be  far  beyond  our  power.  It  is  probably  already  beyond 
the  conceit  of  all  but  the  most  contented  ignorance. 
The  purpose  of  thus  reviewing  the  fundamental  types 
of  argument  is,  then,  that  we  may  be  able  to  catalogue 
their  special  dangers,  so  that,  meeting  with  any  argu- 
ment, we  may  obtain  some  guide  to  the  points  at  which 
to  look  for  weakness :  and,  at  the  same  time,  it  is  in- 
tended to  bring  these  special  dangers  under  a  more 
general  view. 

§  2.  Demonstration  and  Real  Proof. 

For  such  a  purpose,  however,  many  of  the  distinctions 
made,  both  in  the  traditional  logic  and  in  common  usage, 
may  be  left  out  of  consideration :  for  example,  the  dis- 
tinction between  'Demonstration*  and  other  kinds  of 
Proofl 


204  FALLACIEa  [Part  II. 

'  K,*  it  will  be  remembered,  means  'Reason  (or  reasons) 
actually  given ; '  and  R  may  therefore  either  contain  in 
itself  both  Principle  and  Application,  or  may  express  (or 
even  suggest)  only  one  of  these,  leaving  the  other  im- 
plied. In  other  words,  the  proposition  R  — >  T,  implied 
in  every  argument,  may  mean  one  of  two  things : — 
either  (1)  that  R  includes  T  in  its  meaning,  so  that  R 
being  given,  T  may  be  known  by  a  mere  process  of  in- 
terpretation :  or  (2)  that  the  truth  of  R  may  be  accepted 
as  a  sign  that  T  is  able  to  stand  against  adverse  criticism. 
In  the  former  case,  the  argument  is  technically  called  a 
'Demonstration,'  or  complete  Syllogistic  proof;  in  the 
latter  case  there  is,  I  believe,  at  present  no  strict  technical 
name,  but  for  our  present  purposes  I  propose  to  call  such 
arguments  (by  far  the  commonest  in  practice)  Real  argu- 
ments, whether  empirical  (including  analogical  and  in- 
ductive) or  deductive.  The  distinction  between  Demon- 
stration and  Real  Proof  bears  a  certain  likeness  to  that 
between  Tautologous  and  Real  propositions,  already  dis- 
cussed (p.  42).  Just  as  in  the  one  case  the  proposition 
as  a  whole  gives  us  no  more  information  than  is  con- 
veyed by  the  S  alone,  so  in  the  other  case  the  argument 
as  a  whole  makes  no  real  advance  upon  the  Reason 
given. 

The  name  Demonstration  is  perhaps  not  quite  free 
from  ambiguity.  The  popular  notion  of  its  meaning 
seems  to  be  much  the  same  as  *  unanswerable,*  or  *  con- 
clusive,* or  '  complete.'  When  the  illogical  person  finds 
some  theory  no  longer  defensible,  he  not  unf requently 


Chap.  IV.]       THE  EMPLOYMENT  OF  GUESSWORK.  205 

takes  refuge  in  the  disclaimer,  "Of  course  I  cannot 
demonstrate  it,  with  mathematical  certainty:  the  case 
does  not  admit  of  demonstration" — thereby  implying, 
amongst  other  things,  that  if  it  were  'demonstrable,' 
there  could  no  longer  be  any  question  raised  about  its 
truth,  and  that  all  that  the  disputer  has  done  is  to 
demolish  this  impossibly  perfect  kind  of  certainty,  leaving 
the  practical  certainty  intact.  In  this  sense,  probably, 
the  following  passage  was  written, — "However  much 
one  may  be  unable  logically  to  demonstrate  that  there  is 
such  a  thing  as  luck,  there  can  be  no  question  as  to  the 
fact  of  its  existence."  If  the  word  'demonstration' 
means  anything,  it  is  thought,  surely  it  must  mean  com- 
plete and  conclusive  proof.  And  hence,  by  a  curious 
piece  of  inconsistency,  the  name  often  works  round 
again,  in  popular  usage,  to  mean  proof  which  is  *  suf- 
ciently '  or  '  practically '  conclusive ; — as,  for  instance,  in 
the  case  of  a  criminal  caught  redhanded  in  the  act, 
whose  guilt  would  be  commonly  said  to  be  *  demon- 
strated,' 

Complete  and  conclusive,  in  a  manner.  Demonstration 
(in  its  technical  meaning)  certainly  is.  It  is  formally 
complete,  and  it  is  conclusive  as  against  all  who  admit 
the  material  truth  of  the  premisses.  It  is,  in  fact,  an 
unanswerable  argunientum  ad  hominem,  and,  so  far  as 
mankind  agree  about  the  truths  which  may  be  un- 
questionably accepted,  so  far  but  no  further  reaches  its 
universal  binding  force.  Hence  its  especial  connexion, 
in  the  popular  view,  with  mathematics, — the  simplest 


206  FALLACIES.  [Part  IL 

example  of  its  operation.  The  axioms  of  mathematics 
do  not  need  to  be  reconsidered  (even  if  we  have  the 
power  really  to  do  so),  and  so  far  as  Demonstration 
appeals  to  them,  so  far  it  is  conclusive  as  against  all  of 
us.  But  wherever  any  premiss,  whether  in  a  Demon- 
stration or  in  other  kinds  of  Proof,  meets  with  any  doubt 
as  to  its  material  truth,  the  conclusiveness  of  the  argu- 
ment depends  entirely  on  such  doubt  being  cleared  away : 
a  preliminary  question  is  raised,  which,  unless  answered 
satisfactorily,  will  destroy  the  material  cogency  of  the 
Demonstration.  Hence  the  real  force  of  Demonstration 
rests  ultimately  on  the  same  basis  as  that  of  all  other 
kinds  of  argument,  and  reaches  exactly  the  same  level  of 
objective  cogency.  Demonstration  says,  in  fact,  '  You 
admit  the  truth  of  the  thesis  indirectly,  since  you  have 
already  admitted  the  truth  of  this  and  this,  which  to- 
gether include  or  imply  it,'  For,  unless  the  premisses 
are  supposed  to  be  admitted  true,  to  assert  them  as  un- 
assailable reasons  for  believing  the  conclusion  would 
clearly  constitute  an  insidious  kind  of  '  begging  the 
question  at  issue.'  On  this  account,  therefore.  Demon- 
strative Proof  is,  as  a  rule,  less  easy  to  obtain  than  Real 
Proof ;  for  to  obtain  it,  means,  in  fact,  to  obtain  a  person's 
consent  to  the  conclusion  without  his  knowledge. 

If  there  were  any  firm  and  sharp  line  to  be  drawn 
between  absolutely  binding  proof,  and  proof  tainted  with 
human  fallibility,  each  kind  standing  on  opposite  sides 
of  a  clear-cut  chasm,  then  the  name  Demonstration  might 
indeed  be  applied  in  its  dictionary  meaning.     But  as  it 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWORK.  207 

is,  the  limits  of  'axiom'  and  theory'  are  too  ill-defined 
and  undefinable,  one  man's  meat  in  this  respect  being 
too  often  another  man's  poison.  Even  our  senses — 
that  is,  our  'direct  perceptions,'  which  always  include 
an  element  of  inference, — are,  it  need  hardly  be  said, 
liable  to  illusion :  much  more  so  is  the  complicated 
mental  process  by  which  we  recognise  a  '  fact '  as  con- 
clusively certain.  Many  an  innocent  person  has  before 
now  been  "  caught  redhanded  in  the  act."  Accordingly, 
the  nearest  approach  which  we  can  make  towards  apply- 
ing the  name  Demonstration  in  its  etymological  meaning, 
and  at  the  same  time  preserving  its  definiteness  of  out- 
line, is  to  employ  it  for  the  kind  of  certainty  which, 
though  materially  fictitious,  is  formally  complete  ;  which, 
though  not  guarded  absolutely  against  all  possibility  of 
error,  is  guarded  against  it  on  condition  of  the  premisses 
being  materially  true.  And  it  is  probably  on  this  account 
that  the  name  has  been  in  Logic  technically  restricted  to 
complete  Syllogism. 

Technically  then  only  those  arguments  are  demonstra- 
tive in  which  the  thesis  is  included  in  the  meaning  of 
the  reason  or  reasons  given.  Logical  necessity  is  merely 
the  necessity  of  avoiding  self-contradiction,  for  the 
purpose  of  preserving  a  consistent  meaning :  '  necessary 
truth'  is  merely  truth  which  is  already  admitted  in 
another  (usually  a  more  circuitous)  form.  Thus  the 
truth  that  two  and  two  make  four  is  already  admitted 
in  the  full  definition  of  the  terms  employed.  If  at  least 
there  be   anything  more   in   'necessity'   than  is  here 


208  FALLACIES.  [Part  IL 

claimed  for  it,  it  is  something  of  no  importance  to  our 
present  purpose. 

Strictly  speaking,  Demonstration  is  of  two  kinds, — 
Immediate  and  Mediate  (without  or  with  a  'middle 
term '  *).  Hence  I  have  said  in  the  last  paragraph 
'  reason  or  reasons.'  But  in  practice,  when  challenged  to 
prove  an  assertion,  one  has  seldom  the  chance  of  appeal- 
ing to  a  simple  equivalent  form  which  is  already  admitted 
true ;  for  the  obvious  reason  that  '  immediate  inference '  is 
so  extremely  easy  that  the  person  admitting  the  equiva- 
lent form  is  not  likely  to  challenge  the  thesis  itself. 
Mere  rarity  of  occurrence  would  indeed  be  no  ground  for 
neglecting  all  exposition  of  this  mode  of  proof,  if  it  were 
not  for  the  fact  that  indirectly  we  have  already  had 
plentiful  occasion  to  exhaust  the  subject  so  far  as  our 
purposes  demand.  The  sole  equivalent  form  of  any  pro- 
position, apart  from  such  equivalence  as  is  merely  due  to 
synonymous  words  or  to  variations  in  grammatical 
structure,  is  that  already  spoken  of  under  the  '  Law  of 
Counter-indication,'  and  it  seems  unnecessary  to  add 
that  any  assertion  includes  a  denial  of  all  other  assertions 
that  conflict  with  it :  so  that  the  Aristotelian  proposition 
I  is  included  in  A,  and  O  in  E ;  for  this  is  implied  in 
the  full  interpretation  of  the  Maxims  of  Consistency. 

Now  when  the  Reason  contains  expressly  both  a 
principle  and  an  application  of  that  principle  to  the  case 
in  hand,  it  is  clear  that  nothing  more  remains  to  be  done 
than  to  confront  these  two  elements  of  E,  at  once  with 

*  See  pp.  234,  239. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  209 

observed  or  admitted  fact.     That  is  to  say,  the  operation 
of  Logic  as  regards  the  original  Thesis  is  at  an  end,  and 
all  that  remains  to  be  done  is  to  erect,  if  necessary,  these 
two  elements  (the  Principle  and  the  Application)  into 
theses  themselves.    But  occasionally  it  happens  that  such 
complete  Demonstration  is  erroneously  supposed  to  be 
present :  and  then  we  have  either  what  is  sometimes  called 
a  '  Syllogistic  fallacy ',  or  some  misinterpretation  of  the 
language  used,  or,  thirdly,  the  vague  intention  of  raising 
merely  a  '  presumption '  in  favour  of  the  Thesis.     It  is  by 
no  means  always  that  we  can  tell  with  even  approximate 
certainty  which  of  these  three  causes  has  been  in  opera- 
tion,— often  all  three  have  had  a  share.    Aristotle  indeed 
declares  that  in  his  day  even  a  mathematician  *  might  be 
deceived  by  the  argument,  "  Every  figure  has  its  three 
angles  equal  to  two  right  angles :  for  every  triangle  has 
its  three  angles,  etc.,  and  every  triangle  is  a  figure : "  and 
in  Plato's  Republic  we  frequently  find  such  arguments 
admitted  as  valid  :  but  this  after  all  amounts  to  no  more 
than  saying  that  inconclusive  demonstration  was  then  in 
fact  often  accepted  for  conclusive, — a  proposition  true 
of  modem  times  also:    as  to  the  exact  cause  of  such 
acceptance,  that  is  another  matter. 

Completely  demonstrative  arguments,  or  those  even 
pretending  to  be  such,  are,  however,  the  exception,  not 
the  rule.  They  are,  in  fact,  seldom  employed  in  serious 
reasoning  (outside  certain  departments  of  mathematics) 
but  are  nowadays  chiefly  confined  to  cases  where  some 

•  Soph.  El.  vi. — Kol  oi  Ttj^ytrai  K<d  BKws  ol  iritrH\iu>vfs. 


210  FALLACIES.  [Pabt  II 

more  or  less  ingenious  quibble  is  plainly  intended, — as 
in  "  Dry  bread  is  better  than  wisdom :  for  dry  bread  is 
better  than  nothing,  and  nothing  is  better  than  wisdom." 
The  almost  universal  practice  in  these  times  is  to  save 
circumlocution  by  giving  as  Reason  either  the  Principle 
or  the  Application  (more  commonly  the  latter),  but  not 
both  together.  In  the  case  of  'chain  arguments' — 
perhaps  the  commonest  arguments  of  all — the  Reason 
becomes  as  a  rule  still  more  elliptical ;  for  we  there  give 
expressly  neither  the  Principle  itself,  nor  its  application, 
but  merely  the  Reason  which  appears  to  be  chiefly 
needed  in  support  of  one  of  these.  Take  for  instance  the 
not  very  complicated  argument  in  favour  of  Home  Rule 
in  Ireland,  that  "Federalism  is  the  finished  product  of 
civilisation  and  political  ingenuity,"  and  consider  the 
further  suppressed  links  required  to  complete  its  cogency. 
Three  at  least  may  be  at  once  very  easily  distinguished, 
— the  Principle  that  "  to  be  the  finished  product  of,  etc., 
— >  desirability,"  and  two  other  propositions  to  complete 
the  complex  Application  of  such  principle  to  the  present 
case, — "  Home  Rule  — >  separation  of  Imperial  from 
National  and  Local  questions,"  and  "  separation  of,  etc., 
etc.,  — >  Federalism," — none  of  which  appear  in  the 
express  statement.  In  many  actual  arguments,  of  course, 
the  suppressed  links  are  far  more  complicated,  as  in — 
"  Tithes  really  fall  on  the  landlord ;  for  the  rent  of  tithe- 
free  land  is  higher  than  that  of  land  of  the  same  quality 
and  the  same  advantages  of  position  subject  to  tithe," — 
where  a  considerable  amount  of  special  knowledge  of 


Chap,  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  211 

the  subject  is  required  in  order  to  properly  disentangle 
all  the  propositions  implied. 

These  chain  arguments  need  not,  however,  become  in 
any  way  a  stumbling-block ;  since  where  we  do  not  at 
once  see  all  the  hidden  implications,  there  is  a  very 
simple  means  ready  at  hand  for  arriving  at  them.  How- 
ever many  links  there  may  be,  they  are  all  capable  of 
being  summed  up  in  the  concise  expression — 


f  "  If  R  then  T,  and         ) 
I  If  not  T,  then  not  R,"  3 


and  we  have  only  to  call  for  the  grounds  on  which  this 
proposition  is  believed,  in  order  to  have  the  links  set  out 
as  fully  as  we  need,  "  How  does  R  prove  T  ? "  we  ask. 
Thus  in  the  example  just  given  a  person  entirely  ignorant 
of  all  the  ordinary  conditions  of  the  tenure  of  land, 
and  of  all  the  deeper  facts  brought  to  light  by  Political 
Economy,  would  be  as  capable  as  any  one  else  of  erecting 
into  a  new  T  the  conneodon  between  the  R  given  and  the 
origiTial  T:  it  would  take  him  longer,  of  course,  to  arrive 
at  the  rights  of  the  matter  than  it  would  take  another 
person  who  had  already  considered  some  of  the  questions 
involved,  since  he  would  have  to  push  inquiry  further 
back  towards  first  principles ;  but  his  present  ignorance 
of  the  subject  is  only  a  temporary  and  removable  bar. 

Such  then  being  the  difference  between  Demonstra- 
tion and  the  other  kinds  of  Proof,  it  is  clear  that  in 
treating  the  opportunities  for  error  that  occur  in  the 
latter  we  really  treat  those  that  occur  in  both.  If,  when 
either  Principle  or  Application  alone  is  given  we  can 


212  FALLACIES.  [Part  IL 

recognize  the  needs  of  formal  adequacy  sufficiently  to 
avoid  accepting  as  further  assertion  a  supposed  Applica- 
tion or  Principle  which  does  not  really  apply,  a  fortiori 
we  are  guarded  against  accepting  two  insufficient  pre- 
misses when  both  are  expressed.  We  shall  accordingly 
dismiss  all  consideration  of  Demonstration  as  such,  and 
confine  attention  to  the  forms  and  the  dangers  of  what 
is  here  called  '  Real  Proof.' 

§  3.  Induction  and  Dediiction. 

In  the  chapter  on  the  Process  of  Proof  in  general,*  it 
was  seen  that  the  real  foundation  of  Proof  is  always  the 
recognition  of  resemblance  and  difference  between  things 
or  events  known,  or  observed,  and  those  which  are  on 
their  trial,  whether  such  recognition  is  based  on  know- 
ledge already  reached,  and  formulated  in  names  or  pro- 
positions, or  on  direct  observation  and  experiment.  In 
proportion  as  we  openly  and  distinctly  refer  to  known 
principles — already  generalised  knowledge — is  Proof  de- 
ductive: in  proportion  as  we  rapidly  and  somewhat 
dimly  frame  new  principles  for  ourselves  from  the  cases 
observed,  is  Proof  inductive,  empirical,  or  (in  its  loosest 
form)  analogical. 

The  whole  history  of  the  rise  and  growth  of  know- 
ledge, it  has  been  also  already  remarked,  is  a  record  of 
fruitful  rivalry  and  interaction  between  two  opposite 
processes.     Observation  of  facts  has  demanded  theory — 

•  Fart  i.  chap.  t. 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWORK.  213 

statement  of  *  laws  *  or  uniformities — to  explain,  and 
even  to  name,  the  things  and  events  observed :  theory 
in  its  turn  has  always  been  more  or  less  liable  to  the 
purging  criticism  of  'fact.'  In  the  strictest  sense,  of 
course,  Deduction  and  Induction  are  modes  of  Inference, 
not  of  Proof  at  all.  Strictly  speaking,  all  Proof,  so  far  as 
really  Proof,  is  deductive.  That  is  to  say,  unless  and  until 
a  supposed  truth  can  be  brought  under  the  shadow  of  some 
more  certain  truth  it  is  merely  self -supporting,  or  circular. 
Unless  we  have  some  more  comprehensive  and  better 
tested  generalisation  within  the  sweep  of  which  to  bring 
our  thesis,  we  reach  no  foundation  broader  than  itself ; 
no  assurance  beyond  what  may  be  derived  from  the  fact 
that  nothing  has  yet  been  found  to  contradict  the  theory. 
But  yet  there  is  a  meaning  in  the  distinction,  and,  with 
certain  limitations  and  apologies,  I  propose  to  make  some 
use  of  it.  Although  the  dependence  of  any  Thesis  on  its 
Reason  must  be  rationalised — i.e.  must  have  the  under- 
lying principle  made  clear — before  the  testing  operation 
can  be  called  complete,  yet  in  regard  to  special  dangers 
it  makes  considerable  difference  whether  the  principle  is 
at  first  definitely  apprehended  or  not, — whether  (as  it  is 
commonly  expressed)  the  Proof  professes  to  rely  upon 
Laws  known  or  supposed  to  be  true,  or  upon  facts  ob- 
served or  supposed  to  be  observed.  We  must  distinguish 
then,  as  far  as  pbssible,  between  that  kind  of  Proof  which 
rests  openly  and  distinctly  upon  already  generalised 
knowledge — Deductive  Proof, — and  that  which  rests 
upon  what  may  be  loosely  described  as  '  isolated  facts,' 


214  FALLACIES.  [Part  II. 

or  'perception  of  resemblance  and  difference,'  or  'ob- 
servation and  experiment/  or  '  circumstantial  evidence,' 
or  however  the  phrase  may  run, — that  which  is  com- 
monly known  in  its  highest  form  as  Inductive  Proof,  and 
in  its  lowest  form  as  the  Argument  from  Analogy. 

The  required  limitations  in  preserving  the  distinction 
appear  to  be,  in  the  first  place,  a  clear  recognition  that 
although  in  Induction  the  Principle,  or  Law,  connecting 
the  cases  observed  with  those  inferred  is  in  the  case  of 
Inference  commonly  dropped  out  of  sight,  or  at  least  left 
highly  indistinct,  yet  the  whole  cogency  of  Inductive 
Proof  depends  upon  the  extent  to  which  such  Principle 
is  first  rendered  definite  and  then  confronted  with  ob- 
servable or  admitted  fact.  So  long  as  the  Principle  is 
left  indistinct,  we  may  be  fighting  under  false  colours — 
misled,  that  is,  by  false  analogies,  or  hampered  by  dis- 
tinctions without  a  difference — in  extending  our  know- 
ledge to  the  supposed  '  parallel  cases,'  or  in  drawing  our 
line  exactly  where  we  do.  There  is,  in  fact,  probably 
no  more  fertile  source  of  real  (as  opposed  to  merely 
verbal)  fallacy  than  just  this  neglect,  or  dread,  of  '  ra- 
tionalising' our  beliefs, — of  bringing  their  underlying 
principles  out  into  the  daylight.  The  name  Inductive, 
then  (as  also  '  empirical '  and  '  analogical '),  is  properly  a 
name  of  a  mode  of  Inference.  It  describes  the  fact  that 
in  arriving  at  our  Thesis  the  Principle  wobs  left  more  indefi- 
nite than  if  we  had  reached  the  Thesis  deductively.  The 
provinces  of  Analogy,  Induction,  and  Deduction  are  thus 
merely  rough  divisions  on  a  scale  :  the  more  definite  the 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  215 

Principle  the  more  the  inference  possesses  the  deductive 
character,  the  less  definite  the  nearer  it  approaches  to 
loose  Analogy.  But  equally  in  deductive  and  in  analo- 
gical arguments,  in  order  to  rationalise  the  belief  the 
underlying  Principle  must  be  made  definite.  The  chief 
value  of  the  distinction,  for  purposes  of  Proof,  is  that  it 
serves  to  call  attention  directly  to  that  part  of  an  argu- 
ment which  stands  in  pressing  need  of  careful  examina- 
tion :  meeting  with  an  empirical  argument  we  may  often' 
shorten  the  process  of  testing  it  by  inquiring  in  the  first 
place  what  the  underlying  Principle  really  is, — how  far 
it  will  bear  reduction  to  definiteness  and  comparison 
with  fact.  Empirical  arguments  are,  too,  so  far  as  em- 
pirical, free  from  mere  snares  of  language, — which  play 
so  large  a  part  in  all  deductive  proof :  their  chief  danger 
may  be  summed  up  as  the  adoption  of  some  theory  with- 
out examining,  or  perhaps  even  seeing,  the  alternatives. 
But  this  will  be  more  fully  discussed  presently. 

The  second  difficulty  in  preserving  the  distinction  lies 
in  the  fact  that  as  a  rule  the  Empirical  and  Deductive 
processes  are  found  in  combination,  both  being  employed 
on  the  same  subject-matter.  Not  only  does  Inductive 
Proof — in  its  higher  forms — ^make  large  use  of  Deduc- 
tion, for  verifying  the  hypotheses  put  forward,  but  all 
Proof,  however  professedly  deductive,  is  in  the  habit 
(at  least  where  the  generalised  knowledge  is  not  very 
firmly  established  in  the  individual  mind)  of  drawing 
much  confidence  from  successful  prediction,  and  even 
from  merely  congruent  facts.     Some  Free-traders,  for 


216  FALLACIES,  [Pabt  II. 

instance,  lacking  robust  faith  in  the  abstract  propositions 
from  which  that  theory  may  be  deduced,  or  failing  to  hold 
them  clearly  in  memory,  are  apt  to  feel  an  accession  of 
security  when  statistics  '  prove  them  right ; '  and  weak 
or  vague  generalisations,  such  as  that  *  Roman  Catholi- 
cism and  national  poverty  go  hand  in  hand,'  commonly 
draw  what  strength  they  possess  jointly  from  the  two 
sources,  prejudice  {i.e.  '  known  law ')  and  observation.  It 
would  certainly  be  hard  to  find  a  single  instance  of  in- 
Jerence,  within  historic  times,  in  which  we  could  say 
beyond  all  doubt  that  Deduction  was  wholly  wanting  or 
had  contributed  nothing  to  the  belief ;  and  since  any  of 
the  causes  of  a  belief  are  liable  to  be  relied  upon  as  reasons 
on  reflection,  it  is  rare  to  find  professed  empirical  proof 
entirely  free  from  the  deductive  element.*  Sometimes, 
no  doubt,  from  one  cause  or  another,  either  method  may 
dwindle  into  insignificance  beside  the  other.  A  great 
many  people,  for  instance,  are  inclined  to  settle  the 
claims  of  ghost  stories  deductively ; — partly  perhaps 
because  they  find  as  a  rule  that  their  hands  are  more  or 
less  hampered  and  their  eyes  rendered  more  or  less  use- 
less, before  they  are  allowed  to  begin  experimentation. 
On  the  other  hand,  in  Meteorology,  from  a  deficiency  of 
known  laws  we  are  thrown  very  much  upon  bare  facts 

♦  Even  in  attempted  Proof  we  commonly  find  the  two  processes 
mingled,  as  where  Parson  Lingon  argues  in  favour  of  cock-fighting,  not 
only  that  under  it  "  England  had  been  prosperous  and  glorious,"  but 
that  "  the  practice  sharpened  the  faculties  of  men,  gratified  the  instincts 
of  the  fowl,  and  carried  out  the  designs  of  heaven  in  its  admirable  device 
of  spurs." 


CiiAP.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  217 

as  recorded  in  statistics ;  what  certainty  we  have  regard- 
ing the  weather  is  mainly  empirical.  In  all  cases  of  real 
proof,  however,  it  is  probable  that  nowadays  both  pro- 
cesses play  some  part. 

These  two  considerations  make  it,  of  course,  extremely 
difficult  in  practice  to  label  every  argument  at  once  with 
one  or  the  other  name.  Sometimes,  as  where  the  Reason 
is  a  direct  statement  of  the  Principle  itself,  or  again  where 
it  consists  of  a  record  of  some  experiment,  no  hesitation 
need  practically  be  felt  as  to  where  the  danger  lies ;  but 
in  a  large  number  of  cases  we  have  no  means  of  deciding 
whether  the  argument  may  best  be  classed  as  empirical, 
or  deductive,  or  both. 

In  those  logical  treatises  in  which  Inference  and  Proof 
are  not  clearly  distinguished,  and  where  consequently  the 
distinction  between  Induction  and  Deduction  occupies 
a  very  prominent  place,  there  seems  to  be  a  desire  to 
restrict  the  name  of  Inductive  Proof  as  far  as  possible 
to  the  establishment  of  laws  by  means  of  isolated  facts. 
Analogical  Proof  to  the  establishment  of  facts  by  means 
of  resembling  facts,  and  Deductive  Proof  to  all  other 
cases.  But  we  have  seen  that  both  Principle  and  Appli- 
cation are  required  for  all  completed  proof  whatever: 
that  is,  until  both  are  brought  to  daylight  and  examined, 
the  testing  of  the  Thesis  remains  unfinished.  Sometimes 
— i.e.  in  Demonstration — both  Principle  and  Application 
are  expressly  given  by  the  Reason ;  at  other  times  one  or 
the  other  only.  But  yet  it  will  not  do  to  say  that  wher- 
ever the  Principle  is  merely  implied  we  have  a  clear  case 


218  FALLACIES.  [Part  IL 

of  Empirical  Proof,  since  it  is  sometimes  through  extreme 
familiarity,  rather  than  through  insufficient  definiteness, 
that  its  statement  is  suppressed ;  as  where  we  argue 
"  The  Pope  is  fallible,  since  he  is  human."  In  many  such 
eases  the  Principle  relied  upon  might  well  be  definitely 
enough  apprehended  to  warrant  our  calling  them  cases  of 
deductive  proof. 

What  then,  it  may  be  asked,  is  left  of  the  distinction 
at  all  ?  Have  not  these  innocent  limitations  and 
apologies  in  fact  proved  too  much  ?  If  we  cannot  tell 
for  certain  in  the  given  case  whether  the  argument  is 
properly  an  empirical  one  or  properly  deductive,  why 
keep  the  names  and  make  a  pretence  of  using  them  ? 

In  the  first  place,  we  are  here  intentionally  seeking  to 
make  the  best  use  of  the  guesswork  system  of  detecting 
Fallacy,  and  with  that  view  may  be  thankful  for  even 
rough  distinctions  suitable  to  the  purpose.  Nor,  because 
the  distinction  breaks  down  when  pressure  is  put  upon 
it,  need  we  consider  it  wholly  worthless.  It  possesses  a 
solid  core  of  applicability,  and  if  we  can  be  content  to 
use  it  as  a  rough  guide  in  finding  the  weak  point  of  an 
argument,  much  value  may  still  be  extracted  from  it  in 
economy  of  time. 

Again,  if  the  names  Induction  and  Deduction  make  us 
think  of  Inference  rather  than  of  Proof,  we  are  not 
obliged-  to  use  them.  However  we  choose  to  name  the 
two  different  kinds  of  arguments,  the  distinction  between 
them  has  a  certain  real  importance,  as  already  shown; 
ajid  all  that  is  intended  to  be  done  with  it  is  to  recognise 


Chap.  VIJ       THE  EMPLOYMENT   OF  GUESSWORK.  219 

that  SO  far  as  the  given  argument  may  be  seen  to  belong 
to  one  or  the  other  class,  so  far  we  are  already  some  way 
on  the  track  of  '  special  dangers.' 

A  thesis,  then,  whether  abstract  or  concrete,  is  some- 
times supported  by  bringing  forward  a  congruent  fact, 
or  a  number  of  congruent  facts :  in  this  case  the  thesis, 
when  abstract  (as  e.g.  the  law  of  Gravitation,  or  of 
Natural  Selection)  is  usually  called  a  theory.  An  abstract 
theory  is  offered  both  as  an  explanation  of  the  facts  on 
which  it  rests  and  as  a  means  of  prediction  in  the  future, 
thus  basing  a  general  law  upon  individual  facts  observed. 
When  the  thesis  is  concrete  it  is  rarely  called  a  theory, 
but  professes  to  argue  direct  from  case  to  case,  by  what 
is  called  Analogy,  or  Resemblance,  or  Extension  to  parallel 
cases. 

Or,  secondly,  a  Thesis,  also  either  abstract  or  concrete, 
is  sometimes  supported  by  appealing,  expressly  or  other- 
wise, to  an  already  recognised  law.  Here  the  Thesis 
(except  when  explanatory)  is  not  as  a  rule  called  a  theory, 
— probably  because  that  name  carries  with  it  by  custom  a 
shade  of  uncertainty,  which  seems  to  throw  unnecessary 
doubts  upon  the  '  already-recognised  law:'  it  is  occasionally 
called  a  'deduction,'  but  more  often  has  no  distinctive 
title.  As  to  the  nature  of  the  Reason,  sometimes  the  law 
itself  is  expressly  mentioned,  but  more  commonly  the  S 
of  the  thesis  is  labelled  with  some  name,  or  said  to  have 
acted  or  suffered  in  some  particular  way  which  is  '  known ' 
to  carry  certain  consequences.  In  other  words,  whenever 
the  Thesis  professes  to  be  deduced  from  some  already- 


220  FALLACIES.  [Part  II. 

framed  law,  the  Reason  either  expressly  mentions  this 
law,  leaving  its  application  implied,  or  it  appeals  to  some 
sign,  expressly  asserted  to  be  present  in  the  given  case, 
leaving  the  universal  trustworthiness  of  such  sign  implied. 
Accordingly,  the  two  main  kinds  of  argument  may  be 
called  respectively  the  Argument  by  Example  and  the 
Argument  by  Sign.  In  the  former  we  rely  primarily  on 
'  facts  *  observed,  no  law  to  cover  the  case  being  as  yet 
distinctly  admitted;  in  the  latter  we  make  use  of  the 
recognised  results  of  past  observation,  whether  registered 
in  express  propositions  or  merely  taken  for  granted  in  the 
meaning  of  the  names  employed. 

§  4.  Certain  Minor  Distinctions.* 

Before  further  subdividing  these  two  main  forms  of 
argument,  it  will  be  well  to  notice  briefly  certain  other 
distinctions  which  are  sometimes  made,  but  which  mark 
difierences  that  are  quite  unimportant  for  our  purpose. 
Thus  we  have  seen  that  the  distinction  between  conxHu- 
sive  and  presumptive  proof,  though  useful  perhaps  before 
inquiry  begins,  is  altogether  too  loose  for  adoption  into 
Logic.  In  one  sense  no  proof  is  conclusive,  in  another 
sense  unless  proof  professes  to  conclude  the  inquiry  it  is 
not  proof  at  aU.     Really,  the  distinction  seems  to  be 

*  This  section  contains  several  technicalities  which  conld  not  be 
explained,  or  omitted,  without  considerably  lengthening  the  exposition, 
and  it  seemed  desirable  to  save  space  as  ranch  as  possible,  since  the 
section  is  not  essential  to  the  main  thread  of  our  snbject.  The  techni- 
calities  can  be  easily  found  in  any  logical  text-book. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  221 

intended  to  mark  roughly  the  difference  between  a  Thesis 
asserted  and  one  that  is  merely  suggested;  and  such 
hesitating  theses  lie  quite  outside  our  present  interests. 
Further,  certain  names,  such  as  circumstantial  evidence, 
are  almost  synonymous  with  others  that  will  here  be 
employed;  empirical  evidence  including  circumstantial 
evidence  as  the  whole  includes  the  part.  Again, '  testi- 
mony,' '  hearsay  evidence,'  etc.,  though  marking  distinc- 
tions valuable  perhaps  for  some  purposes,  are  varieties 
which  do  not  readily  admit  of  any  special  treatment, 
except  where  there  exists,  as  in  Law,  some  authority 
competent  to  lay  down  strict  rules  with  a  merely  average 
balance  of  good  result.  Logic  is  less  pressed  for  time 
than  Law,  and  can  afford  to  decline  to  generalise  where 
generalisation  is  only  so  roughly  justified. 

Again,  there  is  the  distinction  between  hypothetical 
arguments  and  those  which  are  commonly  called  cate- 
gorical. A  hypothetical  argument,  of  whatever  kind,  is 
simply  one  in  which  the  major  premiss  (the  Principle) 
takes  the  form  of  a  hypothetical  proposition.  The  dif- 
ference between  a  categorical  and  a  hypothetical  propo- 
sition is,  we  have  seen,  merely  a  grammatical  one, 
conveying  at  least  no  difference  of  meaning  that  is  of 
importance  to  our  vicvv  of  Logic.  Any  categorical  argu- 
ment may  therefore  be  expressed  ifi  hypothetical  form, 
and  vice  versd.  While,  however,  the  danger  in  hypo- 
thetical and  in  categorical  arguments  is  essentially  and 
fundamentally  the  same,  the  language  in  which  it  has  to 

be  described  is,  under  the  predication  view,  somewhat 
11 


222  FALLACIES.  [Part  II. 

different.  The  hypothetical  proposition  divides  into  Ante- 
cedent and  Consequent  more  naturally  and  readily  than 
into  S  and  P,  and  accordingly  the  '  middle  term '  of  a 
hypothetical  argument  is  hard  to  find, — or  rather  it 
seems  almost  a  straining  of  language  to  call  it  a  middle 
term  at  all.*  In  a  categorical  argument  the  middle  term 
of  the  Syllogism  involved  is  often  difiicult  enough  to 
disentangle  clearly,  f  but  since  in  hypothetical  arguments 
the  middle  'term'  is  itself  a  proposition,  namely,  the 
Antecedent  (or,  for  a  negative  conclusion,  the  denial  of 
the  Consequent)  of  the  Principle,  any  search  for  the 
middle  term,  as  such,  is  more  often  a  source  of  confusion 
than  of  help.  In  fact,  in  all  cases  of  difficulty,  translation 
from  the  categorical  into  the  hypothetical  form  wUl,  I 
think,  be  found  the  easier  plan,  for  then  we  have  merely 
to  see  whether  or  no  the  minor  premiss  properly  affirms 
the  Antecedent  (or  denies  the  Consequent),  or  improperly 
denies  the  Antecedent  (or  affirms  the  Consequent).  The 
fallacy  of  'affirming  the  Consequent'  in  hypothetical 
argument  is  essentially  the  same  as  that  of  employing 
an  '  midistributed  middle '  in  a  categorical  one ;  and  in 
like  manner  it  may  be  shown  that  '  denying  the  Ante- 

♦  See  also  Bain's  Logic,  bk.  i.  chap.  iii.  sect.  30. 

t  As,  e.g.  in  the  argument  from  difference — Cesare  or  Camestres — 
where,  in  order  to  bring  M  to  the  position  required,  we  have  to  contra- 
posit  the  major  premiss.  Let  the  T  be  '  Whales  are  not  fishes,*  and  the 
R  '  they  cannot  remain  always  under  water,'  the  principle  involved  is 
clearly,  '  Fishes  proper  can  remain,  etc. ;  *  but  it  is  only  in  the  contra- 
positive  form — viz.  *  That  which  cannot  remain,  etc.,  is  not  a  fish,'  that 
we  can  bring  the  middle  term  into  the  position  required. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  223 

cedent '  is  essentially  the  same  as  *  illicit  process  of  the 
major.'  But  in  order  to  describe  the  danger  in  these 
cases  in  the  words  that  are  most  simply  and  naturally 
applicable  to  them,  it  seems  better  to  preserve  the  dis- 
tinction, merely  noting  that  it  is  of  grammatical  rather 
than  logical  interest. 

Of  further  varieties  of  argument  the  complete  list 
would  be  a  very  long  one.  Numerous  small  distinctions, 
unnecessary  for  our  purposes,  have  been  made  from  time 
to  time.  Thus  we  have  the  nineteen  valid  moods  of  the 
Syllogism  (several  of  which  never  really  occur  in  prac- 
tice), or  again  the  argumenta  ad  persoTuiTn,  ad  verecun- 
diam,  ad  populuTn,  etc. — names  which  imply  a  large 
amount  of  insight  into  other  people's  motives.  As  regards 
the  Syllogistic  moods,  while  preserving  to  some  extent 
the  differences  on  which  they  are  founded,  we  may  reduce 
their  number  considerably.  In  fact,  under  the  liberal 
treatment  here  adopted  towards  the  exact  words  in 
which  any  assertion  may  happen  to  be  clothed,  some 
simplification  in  this  respect  follows  of  necessity.  Thus, 
while  we  shall  be  obliged  *  to  take  some  account  of  the 
difference  between  an  affirmative  and  a  negative  Thesis, 
we  do  not  need  to  distinguish  in  every  case  a  negative 
proposition,  as  understood  in  the  Aristotelian  scheme 
from  a  positive  one ;  and  again,  every  '  particular '  pro- 
position, so  far  as  it  makes  a  tangible  assertion  at  all,  is 
negative  in  our  sense.  A  negative  proposition,  as  we 
have  elected  to  understand  it,  is  only  a  proposition  which 
•  Seep.  243. 


224  FALLACIES.  tPABTir. 

intends  to  deny  some  positive  assertion  already  made 
or  believed,  not  every  proposition  which  happens  to 
contain  the  negative  particle,  in  however  close  connexion 
with  its  verb.  The  traditional  mood  Celarent,  for  ex- 
ample, is  probably  hardly  ever  used  for  Disproof,  Camenes 
probably  never  used  at  all.  And,  as  will  be  seen  later,* 
all  the  fourteen  syllogistic  moods  with  the  conclusion  in 
I  or  O  may  be  conveniently  reduced  to  two. 

The  remaining  distinctions  we  shall  have  to  make 
will  be  entirely  within  the  two  main  types,  the  Argument 
by  Example,  and  the  Argument  by  Sign ;  and  they  are 
set  out  in  a  table  (IV.)  in  the  Appendix  (E),  which  may 
be  usefully  kept  in  view  during  our  discussion  of  the 
special  types  of  argument. 


§  5.  The  Argument  hy  Example. 

What  is  here  called  the  Argument  by  Example,  or  by 
*  Congruent  Fact,'  is  not  quite  the  same  as  that  which 
is  commonly  known  as  Proof  by  Circumstantial  Evidence, 
though  closely  similar :  on  the  surface  at  least,  the  latter 
mode  of  argument  relies  upon  facts  (i.e.  circumstances) 
which  together  confirm,  the  Thesis,  It  is  difficult,  indeed, 
to  say  precisely  what  is  '  commonly  known '  under  the 
name  Circumstantial  Evidence,  since  popular  usage  seems 
to  vary.  The  common  acceptation  of  the  term  is,  how- 
ever, almost  certainly,  somewhat  narrower  than  that  to 
*  Cf.  infra,  p.  241,  and  Appendix  (0). 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  225 

which  its  literal  (i.e.  derivational)  meaning  would  point. 
Literallj'-,  circumstantial    evidence  should  include,   one 
supposes,  every  case  of  proof  from  the  circumstances  (or 
aggregate  of  isolated  facts)  observable  or  known :  so  that 
(1)  a  geological  explanation,  founded  on  Nature's  foot- 
prints,  or  (2)  our  opinion   of  a  neighbour's  character, 
founded  on  his  general  conduct,  or  (3)  a  political  pre- 
diction, founded  on  the  signs  of  the  times,  or  (4)  any  law 
of  nature,  founded  on  wide  observation  and  experiment, 
would  all  equally  come  under  the  title.     But  no  doubt 
such  an  employment  of  the  term  would  be  considered  a 
straining  of  language.    The  name  circumstantial  evidence 
shows  a  decided  tendency  to  restrict  itself,  in  common 
usage,  if  not  solely  to  the  case  where  a  crime  is  traced 
home  to  the  criminal  by  means  of  the  marks  that  he  (oi 
his  act)  has  left  behind  him,  at  any  rate  to  proof  of  the 
caiise   of  a   concrete   fact  where  the  evidence  of  eye- 
witnesses cannot  be  obtained,  and  where  the   circum- 
stances are  singly  weak.     In  Law,  of  course,  the  reason 
for  the  importance  given  to  this  distinction  is  mainly 
the   recognition   that   '  facts  may  bear  more  than  one 
interpretation,'  while  direct  testimony  is,  in  the  large 
majority  of  cases,  free  from  all  danger  except  that  of 
deliberate  perjury. 

Under  Proof  by  Example,  however,  will  be  here  in- 
cluded all  cases  where  a  proposition,  whether  abstract  or 
concrete,  is  supported  by  the  production  of  a  fact,  or  of 
facts,  which  are  simply  given  as  agreeing  with  the  theory, 
or  as  forming  cases  under  it,  when  at  the  same  time  it  is 


226  FALLACIES.  [Pabt  II. 

recognised  that  there  is  as  yet  no  definitely  known  Law 
in  the  matter,  to  which  appeal  can  be  directly  made. 
The  primary  danger  in  all  such  cases  is  the  same, — 
namely,  that  the  fact  or  facts  produced  will  admit  of 
some  other  interpretation  than  that  put  upon  them  by 
the  theory.  But  this  danger  takes  certain  special 
shapes,  which  it  will  be  worth  while  to  consider  more  in 
detail.  The  subdivision  to  be  made  under  the  Argument 
by  Example  is  that  into  : — 

(a)  The  Argument  by  Analogy. 

(6)  Proof  of  a  Generalisation,  by  the  facts  which  it 
is  intended  to  explain. 

The  first  of  these  is  what  we  have  already  had  occasion 
to  notice  (p.  104)  as  '  extension  to  parallel  cases ; '  the 
second  embraces  what  are  commonly  known  as  the  pro- 
blems of  Induction, — so  far  as  Proof  is  concerned. 

(a)  The  Argument  hy  Analogy. 

Analogical  reasoning,  or  the  argument  from  indistinct 
resemblance,  is  one  of  the  most  difficult  subjects  to  treat 
with  satisfactory  completeness,  since  arguments  of  ap- 
parently the  most  diverse  forms  are  apt  to  contain  more 
or  less  of  it,  and  on  the  other  hand  we  rarely  meet  with 
a  case  of  open  reliance  on  Analogy  pure  and  simple. 
That  is  to  say,  where  we  do  find  Analogy  unmistakably 
employed,  there  is  also  commonly  a  strong  inclination 
either  to  soften  the  force  of  the  assertion  made  in  the 
Thesis,  so  that  the  process  should  be  viewed  less  as  an 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWORK.  227 

attempt  at  proof  than  as  a  mild  suggestion ;  or  else  to 
put  forward  the  analogy  rather  by  way  of  illustration 
than  as  evidence. 

It  was  not  without  a  reason  that  we  avoided  choosing 
a  symbol  for  the  assertion  of  indistinct  resemblance 
between  S  and  ^.  For  essential  resemblance,  it  will  be 
remembered,  we  found  *  a  symbol  (the  now  familiar 
— >) ;  but  for  the  too  common  assertion  '  S  is  strikingly 
like  ^,'  our  scheme  provides  no  place.  The  reason  is 
that  this  vague  assertion  can  only  be  conceived  as  ac- 
quiring a  practical  value  for  Proof  (valuable  though  it 
may  always  be  for  Discovery)  by  emerging  from  its  safe 
obscurity  through  the  claimed  resemblance  ceasing  to  be 
any  longer  indistinct. 

Resemblance,  it  is  on  all  hands  admitted,  varies  in 
degree.  A  given  individual,  we  say,  for  instance,  is 
more  like  his  father  than  his  mother;  distantly  re- 
sembles a  cousin;  and  still  more  faintly,  a  stranger,  a 
savage,  or  some  particular  animal.  A  cloud  in  the 
sky  may  bear  a  fancied  resemblance  to  some  familiar 
object,  but  not  so  close  a  resemblance  as  one  pea  bears 
to  another.  Now  the  only  manner  in  which  gradual 
variation  can  be  represented  seems  to  be  by  means  of 
numbers, — or  at  least  of  pictures  with  measurable  pro- 
portions,— and  measure  implies  the  conception  of  relative 
number.  Hence,  it  seems,  we  are  driven  to  say  that 
resemblance  varies  in  some  manner  expressible  (if  at  all) 
by  means  of  numbers. 

•  Beop.Bi. 


223  FALLACIES.  [Paet  U. 

To  meet  the  needs  of  accurate  comparison,  we  have 
accordingly  established  the  familiar  phrase  '  iioints  of 
resemblance.'  John  resembles  his  father  in  the  eyes, 
or  hands,  or  hair :  he  has  his  mother's  accent,  and  a  touch 
of  his  grandfather's  gout :  holds  the  same  opinion  as  his 
friend  on  a  certain  important  question ;  has  a  less  hasty 
temper  than  his  enemy ;  and  it  is  in  '  expression '  only 
that  he  resembles  a  mastiff  or  a  bull. 

But  what  are  these  so-called  '  points '  ?  Are  they 
simple  units,  which  have  only  to  be  counted,  for  and 
against,  in  order  to  work  the  sum  by  straightforward 
addition  and  subtraction  ?  I  fear  it  is  not  always  easy  to 
avoid  all  taint  of  this  plausible  eiTor.  Accurate  measure- 
ment seems  at  first  sight  to  demand  equality  of  units. 

The  fact  appears  to  be,  however,  that  no  so-called 
'  point '  of  resemblance  or  difierence  is  known  to  exist 
which  is  not  in  theory  further  analysable,  and  few  that 
are  ultimate  even  to  the  naked  eye.  The  colour  of  the 
eyes,  for  example  (to  choose  out  of  the  list  just  given 
the  point  which  seems  on  the  whole  least  likely  to  jdeld 
further  component  parts),  may  be  broadly  classed  as 
blue  or  brown  or  black  and  so  on;  but  it  can  hardly 
be  disputed  that  between  these  rough  distinctions,  end- 
less shades  of  difference  are  possible.  As  for  accent, 
liability  to  gout,  similarity  of  opinion,  or  of  temper,  or 
of  expression,  each  of  these  is  plainly  seen  to  be  built  up 
of  innumerable  components;  the  numerical  diflSculty  is 
only  verbally  solved  and  really  shelved,  by  determining 
to  treat  any  given  '  point '  as  ultimate. 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWORK.  229 

If  we  cannot  then  arrive  at  valuable  results  by  simply 
counting  the  points  of  resemblance  and  difference,  as  we 
count  black  and  white  balls  in  a  ballot-box,  what  other 
resource  is  open  ?  Only  one ;  namely  to  estimate  as  well 
as  we  can  their  relative  iTnportance  as  regards  the  matter 
in  hand.  For  this  purpose  the  phrase  *  essential  points ' 
has  been  invented.  'Essential  resemblance'  means  're- 
semblance in  the  point  (or  group  of  points)  M,*  which 
is  essential ; '  and  by  essential  is  here  simply  meant 
'sufficient  to  prove  a  certain  other  assertion'  to  which 
reference  is  thus  indirectly  made.  Without  this  indirect 
reference  to  some  further  proposition,  the  phrase  '  essen- 
tial resemblance'  becomes,  not  perhaps  quite  meaning- 
less, but  deprived  of  any  meaning  that  exists  in  definite 
shape:  for  to  reduce  it  to  definiteness  would  be  just  to 
state  wherein  the  essentiality  consists.  It  has  been 
sometimes  said,  for  instance,  that  the  State  essentially 
resembles  a  family ;  and  vaguely  every  schoolboy  can 
see  the  likeness  at  once.  But  beyond  a  mere  oriental 
delight  in  simile  for  its  own  sake  ;  and  beyond  the  hazy 
satisfaction  which  is  still  apt  to  follow  even  the  cheapest 
attempt  to  classify;  when  we  push  the  question  home, 
and  ask  what  exactly  is  intended  to  be  conveyed  by  the 
assertion,  we  find  ourselves  really  hoping,  by  means  of 
the  asserted  resemblance,  to  register  our  right  of  arguing 
(within  certain  indefinite  limits)  from  family  to  State ; 

*  The  symbol  M  (Middle  term)  is  here  chosen  in  reference  to  the 
manner  in  which  the  fundamental  structure  of  the  analogical  ai'gument 
oorresponds  to  that  of  the  deductive  one.     See  also  pp.  232,  234. 


230  FALLACIES.  [Part  II. 

that  is,  of  saying  that  since  some  given  assertion  may 
be  made  about  the  former  it  may  also  be  made  about  the 
latter.  It  is  this  further  assertion,  whether  clearly 
apprehended  as  the  purpose  or  (more  commonly)  not, 
to  which  the  '  essential '  refers  :  and  an  '  essential  point ' 
is  a  resemblance  or  difference,  wide  or  narrow,  complex 
or  apparently  simple,  that  may  be  used  as  a  sign  of  the 
truth  of  such  proposition. 

As  yet,  however,  the  difficulties  in  fully  understand- 
ing the  analogical  argument  are  hardly  more  than  begun. 
And  first,  as  to  the  symbolic  expression ;  here  some  care 
is  needed  in  order  to  avoid  ambiguities.  It  clearly  will 
not  do  to  use  S  and  ^  as  the  terms  of  both  propositions, 
the  Thesis  and  the  Reason;  but  with  the  aid  of  the 
symbol  Z  in  addition,  we  can  sufficiently  express  all  that 
is  necessary.  If  we  also  use  the  symbol for  Re- 
lation in  general,  the  universal  form  for  the  analogical 
argument  would  run  as  follows  : — 

(Thesis)  S Z ;  for 

(Reason)  ^ Z.* 

This,  it  must  be  confessed,  just  as  MiU's  formula  on 
which  it  is  based,  "f*  is  a  statement  simplified  artificially 
to  the  utmost.    An  actual  analogical  argument  may  be 

*  It  should  be  noticed,  however,  that  this  formnla  is  only  valid  on 

the  condition  that  the  symbol  means  approximately  the  same  in 

Thesis  and  Reason. 

+  Mill's  formnla  is  stated,  however,  as  if  discovery,  not  proof,  were 
chiefly  contemplated.  It  runs,  "  Two  things  resemble  each  other  in 
one  or  more  respects ;  a  certain  proposition  is  true  of  the  one,  therefore 
it  is  true  of  the  other." 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  231 

complicated  by  failure  of  complete  identity  between  Z 
in  Thesis  and  in  Reason,  or  even  perhaps  between  the 
respective  copulas.*  Or  again,  Analogy  is  very  commonly 
employed  as  part  of  a  full  deductive  process,  as  in 
"  Colonies  ought  not  to  rebel  against  the  mother-country, 
since  they  are  (so  to  speak)  its  children,  and  (it  is  an 
accepted  law  that)  children  ought  not  to  rebel  against 
their  parents."  Every  kind  of  argument,  in  fact,  may 
have  an  analogical  element  in  it,  and  wherever  the 
analogical  element  is  present  the  danger  is  to  that  extent 
the  same.  But  this  special  danger  will  be  spoken  of 
later;  at  present  we  have  only  to  set  out  and  describe 
the  various  kinds  of  argument. 

A  more  serious  difficulty  may  be  stated  as  follows : 
If,  as  appears,  what  is  really  relied  upon  in  the  argument 
by  Analogy  is  a  supposed '  essential  resemblance '  between 
S  and  ^,  and  if  by  essential  resemblance  is  meant 
resemblance  in  the  point  M,  such  point  being  claimed  as 
a  sign  for  the  purpose  required  ;  wherein  does  the  attempt 
to  prove  by  analogy  differ  from  the  purely  deductive 
argument  ?  Clearly,  it  may  be  said,  unless  the  resem- 
blance is  declared  essential  for  the  purpose  in  hand  (i.e. 
for  proving  the  Thesis),  there  is  nothing  to  show  the 
relevancy  of  the  argument ;  until  the  points  of  resem- 
blance are  recognised  as  such,  how  can  we  even  begin  to 
inquire  whether  they  are  important  or  wholly  trivial; 
and  if  their  possible  triviality  is  still  an  open  question, 
whence  our  confidence  in  their  binding  force  ? 

*  The  '  copula '  is  the  sign  of  relation.     See  p.  54. 


232  FALLACIES.  tPABT  U. 

The  answer  must  be  that  this  is  exactly  the  question 
which  Logic  has  to  put  to  the  person  whom  an  analogy 
convinces.  The  difference  between  the  analogical  and 
the  deductive  arguments  is  a  difference  in  the  degree  of 
distinctness  with  which  the  existence  of  the  link  M,  and 
the  fact  of  its  being  a  truly  important  link,  are  recognised 
and  appealed  to.  We  need  a  name  by  which  to  describe 
the  cases  where  these  two  opportunities  for  error  have 
been  left  to  take  care  of  themselves, — where  ready  and 
generous  faith,  rather  than  the  cold  and  grudging  spirit 
of  strict  inquiry,  has  been  in  operation, — and  for  this 
purpose  the  name  Analogical  Reasoning  has  won  a  firm 
place  in  our  terminology.  By  analogical  reasoning  we 
denote  what  may  be  called  embryonic  deductive  argu- 
ments,— arguments  which  are  as  yet  in  happy  uncon- 
sciousness of  the  troubles  in  store  for  them  later. 

The  solution  of  the  seeming  paradox  is  therefore  not 
difficult  to  find.  The  argument  from  analogy  is,  properly 
speaking,  not  so  much  a  mode  of  attempting  proof,  as 
a  mode  of  attempting  to  dispense  with  the  serious  labour 
of  proving.  It  lies  at  that  end  of  the  scale  of  cogency 
which  is  furthest  from  Demonstration.  Instead  of  win- 
ning its  results  openly,  in  the  face  of  hostile  criticism, 
it  prefers  the  easier  course  of  simply  claiming  already  to 
hold  them  safe.  It  is  only  this  claim  which  causes  the 
puzzle  just  noticed ;  we  are  apt  to  forget  that  a  claim 
may  be  made  without  any  valid  foundation. 

In  this  connexion,  there  remains  one  further  difficulty, 
though  not  of  any  great  importance.     It  wiU  perhaps  be 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWORK.  233 

doubted  at  first  sight  whether  the  analogical  argument 
should  properly  be  considered  to  come  under  Proof  by 
Example  as  here  understood ;  since,  the  Thesis  being  itself 
the  '  theory,'  the  Reason  is  not  a  '  fact  agreeing  with  the 
theory,'  except  on  condition  that  the  analogy  holds  good  ; 
which  condition  cannot  be  simply  taken  for  granted  with- 
out begging  the  question.  '  ^  — >  Z '  (e.g.)  is  only  a  fact 
agreeing  with  the  theory  that  S  — >  Z,  on  condition  that 
there  is  essential  resemblance  between  S  and  ^ ;  and 
the  question  whether  or  no  this  essential  resemblance 
exists  is  just  the  turning-point  of  the  argument.  But 
the  reason  for  treating  Analogy  as  Congruent  Fact  is 
that  inasmuch  as  the  employment  of  an  analogical  argu- 
ment implies  in  itself  that  the  analogy  is  supposed  (by 
its  employer)  to  be  a  valid  one,  wherever  analogy  is 
appealed  to  as  proof  it  is  clear  that  R  is  given  as  being 
a  fact  agreeing  with  the  theory ;  inasmuch  as  the  case 
given  is  supposed  by  the  arguer  to  be  a  case  in  point, 
the  argument  is  brought  forward  as  resting  on  a  fact 
agreeing  with  the  theory. 

The  central  type  of  Analogical  reasoning  is,  then, 
that  which  we  have  already  briefly  noticed  above  as 
'  Extension  to  parallel  cases.'  Case  S  and  case  ^  being 
seen  to  be  'similar,'  a  certain  assertion  true  of  the  one 
is  supposed  to  be  true  of  the  other.  If  the  sugar  trade 
is  to  be  protected,  why  not  the  iron  trade  or  the  cotton 
trade  ?  Since  the  Irish  Church  has  been  disestablished, 
why  not  the  English  Church  also  ?  Such  examples 
as  these,  however,  lie  on  the  borderland  between  the 


234  FALLACIES.  [Pabt  II. 

arguments  from  analogy  and  from  sign.  The  technical 
distinction  between  the  argument  from  analogy  and 
the  deductive  argument  from  sign  or  mark  (or  middle 
term)  being  that  in  the  former  the  exact  points  of  re- 
semblance and  difference  between  the  things  compared 
are  admittedly  not  yet  distinct,  it  follows  that  so  soon  as 
the  details  of  resemblance  become  clearly  recognised  as  a 
warrant  for  considering  the  cases  parallel,  these  points  of 
community  become  at  once  a  sign  relied  upon,  and  the 
argument  rises  to  the  deductive  rank.  Thus  in  the 
instances  just  given,  if  the  sole  (or  sufficient)  point  of 
resemblance  claimed  be  the  fact  that  both  are  trades  or 
that  both  are  national  Churches,  then  the  assertions  that 
the  sugar  trade  ought  not  to  be  protected  or  that  the 
English  Church  ought  to  be  disestablished,  are  based  no 
longer  on  mere  analogy  but  on  implied  principles  under 
which  they  are  brought  by  means  of  the  respective  signs 
or  middle  terms.  The  case  of  the  sugar  trade  is  in  this 
way  refen-ed  to  the  recognised  principle  that  protected 
trade  is  on  the  whole  uneconomical;  the  case  of  the 
English  Church  is  referred  to  a  precedent  supposed  to 
have  been  created  (i.e.  a  principle  supposed  to  have 
already  received  tacit  recognition)  by  what  has  gone 
before. 

(6)  Proof  of  Law  from  Fact. 

The  second  mode  of  Proof  by  example  is  where  the 
example  or  examples  given  are  not  supposed  parallel 
cases  to  the  theory,  but  instances,  and  if  possible  *  cru- 


Chap.vl]     the  employment  of  guesswork.  235 

cial'*  instances,  of  the  operation  of  the  supposed  law. 
And,  first,  there  is  a  further  simplification  to  be  made, 
after  the  pattern  of  that  used  by  Mill  in  framing  a  uni- 
versal formula  for  Analogy.  The  generalisation  which 
appeals  to  facts  as  evidence  may,  as  we  have  seen  above, 
either  be  expressed  directly  as  an  abstract  proposition, 
or  lie  hid  under  cover  of  a  concrete  or  abstract-concrete 
one.  The  attempt  to  prove,  for  example,  that  S  (a  known 
concrete  event)  was  causally  connected  with  ^  (whether 
the  latter  be  also  known  to  have  existed  or  not)  by 
means  of  some  fact  merely  agreeing  with  such  theory, — 
such  as  that  S  immediately  preceded  or  followed  ^, 
either  in  this  case  or  on  past  occasions — belongs  properly 
to  this  mode  of  argument  just  as  truly  as  the  attempt  to 
prove  by  the  same  means  the  simple  direct  generalisation 
that  S  is  (in  general)  thus  causally  connected  with  ^. 
In  other  words,  the  evidence  produced  for  any  assertion 
may  conceivably  be  (is  sometimes)  of  an  empirical  kind. 
In  supporting  any  variety  of  thesis,  the  exact  law,  or 
outcome  of  conflicting  forces,  relied  upon,  may  be  so 
dimly  conceived  that  to  call  the  process  in  its  present 
stage  deductive  would  be  to  confuse  a  very  important 
distinction,  while  any  attempt  to  search  first  for  the 
faults  to  which  deductive  proof,  as  such,  is  mainly  liable, 
would  be  a  waste  of  time. 

This  being  the  basis  of  the  distinction,  we  shall  find 

•  A  omcial  instance,  in  its  modern  sense,  may  be  defined  as  anj 
single  instance  deemed  sufficient  to  prove  a  law :  as  in  many  cases  of 
Proof  under  the  method  of  Difference.     See  Appendix  (B),  p.  346. 


236  FALLACIES.  [Pabt  IL 

that,  in  attempting  to  frame  a  typical  formula  for  the 
inductive  argument,  it  is  best  to  take  for  the  Thesis  an 
abstract  proposition.  Not  only  are  such  arguments  the 
kind  in  which  the  evidence  is  as  a  fact  most  frequently 
empirical,  but  that  in  which  it  is  most  rightfully  so  :  since 
a  concrete  proposition  that  rests  on  merely  empirical 
grounds  has,  and  is  widely  recognised  as  having,  a  merely 
provisional  support ;  while  it  is  equally  clear  and  also 
sufficiently  widely  recognised  that  our  deepest  basis  for 
abstract  law  is  concrete  fact.  To  deal  with  concrete 
subject-matter  successfully,  in  the  complexity  in  which 
it  actually  occurs, — which  complexity  is  ever  becoming 
more  manifest  as  our  view  opens  out  and  hidden  dif- 
ferences come  to  light, — we  need  at  least  some  glimpse 
of  the  uniformities  concerned,  some  knowledge  of  what 
may  be  expected  a  priori ;  and  this  whether  the  concrete 
Thesis  is  explanatory,  classifying,  or  predictive.  In 
practice  it  is  safe  to  say  that  wherever  a  concrete  Thesis 
is  supported  by  appeal  to  congruent  facts  alone,  the  first 
step  towards  testing  the  value  of  the  evidence  must  be 
to  get  the  supposed  underlying  laws  clearly  stated ;  and 
that  where  an  abstract-concrete  proposition  is  thus  sup- 
ported, it  is  the  abstract  element  in  it  which  stands  first 
in  need  of  proof. 

After  what  has  been  already  said  on  the  subject  of 
Analogy,  this  more  direct  kind  of  generalisation  needs 
little  further  preliminary  notice.  •  Whereas  in  analogical 
reasoning  the  leap  from  one  supposed  parallel  case  to  the 
other  is  made  with  only  a  dim  recognition  of  the  law 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWOBK.  237 

(M  >  Z)  which  should  bind  the  cases  together,  here  we 
have  the  law  itself  directly  set  up  as  Thesis.  5^  has  been 
observed  in  a  certain  connexion  with  Z,  in  certain  cir- 
cumstances which  seem  to  warrant  our  saying  not  only 
that  when  (if  ever)  we  meet  with  ^  again  we  may  look 
for  Z,  but  that  M  was  that  particular  element  of  ^  which 
was  essential,  and  that  the  wider  law  M  — >  Z  can  hold 
its  own  against  all  but  unpractical  doubts. 

Any  '  thing '  we  like  to  name, — let  us  here  name  it  ^ 
— is  analysable  into  component  circumstances.  Let  ^, 
for  example,  be  that  event  called  the  arrival  of  a  ship  at 
St.  Kilda.  Some  time  ago  "it  was  a  general  belief  at 
St.  Kilda  that  the  arrival  of  a  ship  gave  all  the  inhabi- 
tants colds."*  Let  'unusually  numerous  colds  among 
the  inhabitants  *  be  represented  by  Z.  The  inhabitants, 
then,  we  are  told,  commonly  believed  the  truth  either  of 
the  simple  law  §b  — >  Z>  or  possibly  (if  the  material 
framework  of  the  ship  itself  be  denoted  by  M)  the  law 
M  — >  Z.  But  this  easy  explanation  did  not  satisfy 
Dr.  John  Campbell,  and  he  began  to  analyse  ^  a  little 
more  deeply,  and  to  ask  what  distinguishable  circum- 
stances there  were,  forming  part  of  that  which  was 
broadly  described  as  '  the  arrival  of  a  ship ;  *  and  after 
taking  "  a  great  deal  of  pains  "  he  ended  by  explaining  it 
"  as  the  effect  of  effluvia  arising  from  human  bodies."  "We 
are  not  told  more  definitely  what  he  meant  by  this,  or 
why  the  arrival  of  a  single  ship  at  the  harbour  should 

♦  Dr.  Paris,  Pharmacologia,  p.  89,  quoted  by  Prof.  Fowler,  Inductive 
Logic,  p.  310. 


238-  FALLACIES.  [Paet  U. 

mean  so  great  a  difference  in  the  amount  of  effluvium  in 
the  island,  but  at  any  rate  such  was  his  explanation ; 
and  if  we  denote  '  effluvia  arising  from  human  bodies ' 
by  N,  the  law  at  which  he  arrived  was  either '  N  — >  Z/ 
or '5b,  when  N, — >  Z.' 

Dr.  Paris,  however,  either  himself  discovered,  or  at 
least  quotes  and  endorses  the  discovery  of,  another 
element  inseparable  from  ^,  and  in  his  view  more  im- 
portant as  regards  Z.  This  was  the  fact  that  "  the  situa- 
tion of  St.  Kilda  renders  a  north-east  wind  indispensably 
necessary  before  a  stranger  can  land."  Let  N.E.  wind 
be  represented  by  O.  "  The  wind,"  he  adds,  "  not  the 
stranger,  occasioned  the  epidemic ; "  or,  in  other  words, 
he  views  the  real  law  as  O  — >  Z.  This  law,  it  may  be 
usefully  noticed  in  passing,  was  not  then  discovered  for 
the  first  time.  O  was  already  known  as  a  vera  causa  of 
Z,  while  M  and  N  were  not.  If  we  had  no  known  laws 
already,  discovery  of  explanations  would  be  a  slower 
process  than  at  present.  But  Dr.  John  Campbell  had 
left  the  supposed  law  in  an  unsatisfactory  condition :  the 
assertion  ^  N  — >  Z  was  in  possession,  and  it  had  to  be 
made  to  face  a  hitherto  unsuspected  alternative, — ^that 
which  Dr.  Paris  suggested. 

It  seems  hardly  necessary  to  remark  that  the  symbols 
M  and  Z  were  only  chosen  in  order  to  show  more  clearly 
the  connexion  between  Induction  and  Analogy.  But  in 
framing  a  formula  for  the  inductive  argument,  we  may 
now  return  to  S  and  ^,  without  any  danger  of  misinter- 
pretation.   I  do  not  see  how  to  put  the  whole  inductive 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  239 

argument  into  symbols ;  but  we  may  state  it  in  a  con- 
veniently short  form  as : — 

S  (universally)  — >  ^ :  for  here  are  (one  or  more) 

cases  of  which  this  law  is  the  best  explanation : 

proper  precautions  having  been  taken  against  all 

rival  theories. 

The  discussion  of  these  proper  precautions  will  be  more 

in  place  when  we  speak  more  directly  of  the  dangers  of 

Empirical  proof     At  present  there  remain  the  deductive 

arguments  to  set  out 


§  6.  The  Argument  by  Sign. 

In  speaking  of  Analogy,  we  have  already  sufficiently 
noticed  the  indistinctness  of  the  line  between  this  and 
Deductive  Proof,  and  the  manner  in  which  the  analogical 
argument  becomes  deductive  as  soon  as  the  points  of 
supposed  resemblance  between  S  and  ^  are  definitely 
apprehended  as  a  warrant  for  the  inference  And  just 
as  the  analogical  argument  may  apply  to  any  kind  of 
subject-matter,  so  may  the  strictly  deductive  argument. 
We  may  attempt  to  prove  or  to  disprove  either  an  abstract 
or  a  concrete  proposition,  and  either  an  explanatory,  a 
classifying,  or  a  predictive  one,  by  means  of  a  definite 
middle  term.  And,  further,  the  nature  of  this  middle 
term,  or  link,  must  also  already  be  sufficiently  obvious. 
If  it  is  to  be  really  a  link,  it  must  be  a  sign ;  or,  in  other 
words,  it  must  be  known  to  us  (or  expressible)  as  the  S 
of  an  assertive  proposition. 


240  FALLACIES.  [Part  II. 

It  remains  to  be  added,  however,  that  although  in 
every  deductive  argument  M  may  certainly  be  viewed  as 
a  sign,  this  is  not  always  the  most  direct  description  of 
it  that  can  be  given.  Various  types  of  deductive  argu- 
ment are  distinguishable,  and  it  is  only  where  the  Thesis 
is  affirmative  that  we  really  gain  much  by  resting  our 
case  on  plain,  straightforward  indication.  Thus,  where 
the  Thesis  is  'S  (or  This  S)  — >  ^,'  if  we  know  already 
the  law  that  M  — >  ^,  M  is  well  described  as  a  mark 
or  sign  which  it  should  be  our  aim  to  show  that  S  pos- 
sesses. And,  on  the  other  hand,  if  *  S  — >  M '  be  given 
as  a  reason,  the  relevancy  of  such  reason  plainly  depends 
on  the  tnistworthiness  of  M  as  indicating  ^.  This  for- 
mula, it  will  be  seen  at  once  (namely  '  S  — >  ^  :  for 
S  — >  M,  and  M  — >  ^ '),  corresponds  to  the  ancient 
syllogistic  mood  Barbara  (or  to  Celarent,  where  the  E 
conclusion  is  affirmative  in  the  sense  here  used  *),  or,  in 
the  language  of  the  hypothetical  syllogism,  to  the  modus 
ponens.li  Our  known  law  is  that '  if  or  wherever  M  can 
be  indicated,  ^  is  indicated  also,'  and  our  application  is 
that  here,  in  the  case  before  us  (namely  S),  M  can  be 
indicated. 

But  take  next  the  case  where  the  thesis  is  an  '  Asser- 
tion of  Difference,'  as  S  '-*'  ^ :  here  the  word  '  sign '  (in 
its  ordinary  restricted  meaning,  at  least)  is  far  less 
directly  applicable.     To  the  deductive  argument  to  prove 

•  See  pp.  65,  66,  73. 

t  Where  M  is  negative  (i.e.  in  the  disjunctive  argument),  this  is 
called  the  modus  tollendo  ponens. 


Chap.  VL]       THE  EMPLOYMENT  OF  GUESSWORK.  241 

such  a  thesis,  the  name  'Distinction  by  point  of  differ- 
ence '  seems  better  applied :  two  '  things '  are  seen  to  be 
distinct,  since  one  has,  while  the  other  lacks,  a  certain 
quality.     For  example : — 

"  The  release  of  the  Kilmainham  prisoners  was  not  a  case  of  *  pay- 
ing black  mail : '  for  now,  sir  .  .  .  what  is  paying  black  mail  ?  To 
pay  black  mail  is  to  give  something  that  you  would  not  otherwise 
give.     Are  we  going  to  do  so  ?  " 

And  according  as  S  or  ^  is  the  possessor  of  the  quality, 
we  get  two  slightly  different  formulae  : — 

(Cesare)  S  /^  J^ :  for  S  — >  M,  and  ^  — >  non-M : 

{Camestres)  S^^^:  forS  — >  non-M,  and  ^  — >  M : 
or,  expressed  in  hypothetical  form : — 
-     (modus  ponendo  tollens)  S  /^  ^ :  for  if  ^  were  in- 
dicated the  absence  of  M  would  follow  :  but  here  (namely, 
in  the  case  of  S)  the  presence  of  M  is  indicated : 

(modus  tollens)  S  z^*  ^ :  for  if  ^  were  indicated, 
the  presence  of  M  would  follow :  but  here,  the  absence,  etc. 

And,  lastly,  take  the  case  where  the  thesis  is  symbo- 
lized as  S  H — >  ^,* — the  case  where  (by  means  of  a  middle 
term)  an  exception  is  brought  against  some  generalisa- 
tion. It  is  somewhat  difficult  to  frame  any  single  for- 
mula for  this  mode  of  argument,  while  introducing  any 
mention  of  a  middle  term.  But  the  varieties  may  be 
reduced  to  ttvo  that  appear  fundamental,  all  minor  kinds 
being  capable  of  being  shown  to  belong  to  one  or  the 
other.t    These  two  are : — 

*  The  symbol  -|->  was  explained  on  p.  68. 

t  For  the  reduction  of  these  in  detail,  see  Appendix  (C). 


242  FALLACIES.  [Paet  II. 

(1)  S  -1-^  ^:  for  S  -h->  M,and  5b-->  M  {Barolco): 

(2)  S  -H>  S> :  for  M  -|-^  ^,  and  M  — >  S  (BoJcardo). 
The  distinction  made  is  briefly  as  follows :  the  first 

formula  includes  every  case  where,  in  support  of  a  bare 
denial,  some  point  of  difference  is  shown  to  exist  in  one 
or  more  instances  between  S  and  ^  of  the  positive 
assertion  denied,  or  where  S  is  shown  to  possess,  in  one 
or  more  instances,  a  sign  (M,  or  non-M)  of  the  absence  of 
^.  The  second  includes  every  case  where  an  instance, 
or  a  part  of  the  class  spoken  of,  is  brought  forward  as 
contradicting  the  generalisation.  We  may,  for  conve- 
nience call  the  former  'Exceptive  disproof  by  Sign 
or  Difference,'  and  the  latter  '  Exceptive  disproof  by 
Example.'     As  instances,  we  may  take  for  the  former : — 

*'  Quibbling  is  not  necessarily  a  case  of  sophistry :  for  quibbling  may 
be  unintentional,  while  sophistry  always  implies  the  intention  to  deceive." 

Or— 

"Honesty  is  not  always  the  best  policy:  for  honesty  sometimes 
means  starvation  (and  what  ends  in  starvation  is  certainly  not,  etc.)." 

And  for  the  latter — 

"The  radical  is  not  always  a  man  of  lofty  motives:   your  mere 
malcontent,  for  example,  is  often  rather  a  selfish  being,  and  every  mal- 
content is  of  course  a  radical." 
Or— 

"  It  does  not  follow  that  a  stickler  for  truth-telling  need  be  narrow 
and  severe :  quakers,  for  example,  make  a  great  point  of  telling  the 
exact  and  literal  truth,  and  they  are  often  charitable  enough." 

Three  main  kinds,  then,  of  deductive  argument  are 
distinguishable : — 
1.  Proof  by  Sign : 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  243 

2.  Distinction  by  Point  of  Difference  : 

3.  Exceptive  Disproof: 

And  it  has  been  noticed  that  these  three  apply  respec- 
tively to  the  support  of  the  three  different  kinds  of 
thesis,— S  — >  ^,  S  /^  §bj  and  S  -|— >  ^.  It  seems 
necessary,  however,  to  remove  a  possible  misconstruction 
here.  It  must  not  be  supposed  that  Barbara  and  Cdarent 
are  themselves  never  used  in  Disproof,  or  Cesare  and 
Camestres  never  used  in  Proof  On  the  contrary,  both 
Disproof  by  sign,  and  Proof  by  essential  difference  are 
possible.  Thus  we  might  appeal  to  the  sign  that  'his 
hat  is  hanging  on  its  peg,'  in  disproof  of  the  assertion 
*  he  has  gone  into  the  city ; '  or,  on  the  other  hand,  we 
might  prove,  by  means  of  a  point  of  essential  difference, 
the  positive  assertion  that  between  whales  and  fishes  a 
useful  distinction  may  be  made.  But  since  on  the  whole 
the  formula  Barbara  (or  Celarent)  is  more  often  used  to 
support  a  positive  assertion,  while  the  argument  from 
Difference  is  more  often  used  to  support  a  bare  denial  of 
analogy  or  of  superficial  classification,  it  seems  better,  in 
treating  the  special  arguments  broadly  and  typically,  to 
connect  the  former  with  Proof,  the  latter  with  Disproof. 
And  as  regards  the  assertion  S  -\ — >  ^,  although  from 
our  point  of  view  this  may  be  treated  as  purely  negative, 
yet  it  is  undeniable  that  the  vague  and  flimsy  positive 
assertion  which  such  propositions  are  on  occasion  used  to 
express,  may  also  be  supported  by  the  same  evidence  as 
that  employed  to  support  their  meaning  of  bare  but 
downright  denial.     This  verbal  difficulty  need  not,   I 


244  FALLACIES.  [Pabt  II. 

hope,  after  what  has  been  ahready  said  about  the  inter- 
pretation of  grammatical  forms,  occasion  a  real  stum- 
bling-block. And  we  may  now,  before  speaking  of  the 
dangers  of  deduction  as  a  whole,  briefly  discuss  the 
occasions  and  purposes  for  which  each  of  its  three 
typical  forms  is  most  commonly  employed. 


(a)  Proof  hy  Sign. 

In  one  sense,  of  course,  all  attempted  Proof  is  an 
attempt  to  show  signs.  The  Reason  itself  is  always 
given  as  a  supposed  sign  that  the  Thesis  is  true.  But  as 
contrasted  with  Empirical  Proof,  there  need  be  no  danger 
in  restricting  the  name  of  '  Proof  by  Sign '  to  the  cases 
where  the  sign  given  is  plainly  recognised  as  being  such 
in  general ,-  where,  that  is,  a  middle  term  is  in  some  way 
referred  to,  and  where  accordingly  the  attempted  Proof 
approaches  the  deductive  type.  The  distinction  between 
empirical  and  deductive  proof  lies,  as  already  said,  in  the 
fact  that  in  the  latter  the  proposition  stating  the  universal 
trustworthiness  of  the  sign  asserted  has  already  taken 
more  definite  shape  in  the  mind  of  the  person  using  the 
argument.  Where,  as  in  empirical  proof,  we  argue  that 
a  theory  is  true  because  it  is  the  'best  explanation'  of 
certain  facts,  the  proposition  summing  up  the  grounds 
on  which  this  is  taken  to  be  the  best  explanation  is 
nearly  always  too  complicated  to  admit  of  statement 
without  much  preliminary  labour,  if  at  all.  But  so  far 
as  we  refer  to  a  sign,  with  definite  consciousness  that  it 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWOEK.  245 

is  (in  general)  a  sign  of  the  ^,  so  far  the  argument  is 
deductive. 

The  emplojntnent  of  Proof  by  Sign  is  one  of  the  chief 
purposes,  and  clearly  the  directest  purpose,  for  which 
every  abstract  proposition  exists.  In  every  abstract  pro- 
position, something  is  said  universally  to  indicate  (to  be 
a  sign  of)  §^.  And  that  'something'  becomes  thereby 
capable  of  being  made  the  middle  term  in  Proof  by  Sign. 
If,  therefore,  any  S  can  be  identified  with  (or  shown  to 
indicate)  such  M,  it  indicates  also,  of  necessity,  that 
which  the  sign  signifies ;  for  nota  notm  est  nota  rei  ipsius. 

In  a  former  chapter  *  we  saw  that  general  names 
might  be  viewed  as  labels  attached  to  the  '  things '  that 
bear  them,  and  in  Proof  by  Sign  we  have  the  clearest 
instance  of  the  operation  of  the  naming  process.  What- 
ever facts,  positive  and  negative,  are  included  in  the 
meaning  of  a  name,  are  true,  of  course,  of  anything 
which  rightfully  deserves  the  name.  Hence,  in  order 
to  prove  one  of  such  facts  about  a  given  S,  we  need 
only  show  its  rightful  possession  of  that  particular  label. 
While,  then,  this  mode  of  Proof  sometimes  proceeds  by 
stating  both  Principle  and  Application  (full  Demonstra- 
tion), and  sometimes  by  stating  the  Principle  only,  the 
commonest  form  is  where  the  Reason  states  that  S  de- 
serves (or,  for  the  disjunctive  argument,  does  not  deserve) 
the  name  of  M. 

Proof  by  Sign  is,  in  fact,  so  familiar  and  so  funda- 
mental a  process  that  it  seems  hardly  worth  while  to 

*  See  p.  109,  above. 
12 


246  FALLACIES.  [Part  II. 

spend  more  time  in  merely  describing  it.  The  dangers 
to  which  it  is  liable  are  our  real  concern,  and  these  will 
be  spoken  of  presently.  But  the  other  two  modes  of 
deductive  argument  call  for  a  few  words  of  further 
description. 

(6)  Distinction  by  Point  of  Difference. 

The  exact  point  of  difference  between  S  and  ^  is 
sometimes  just  as  dimly  conceived  as  is  the  resemblance 
relied  upon  in  the  Argument  by  Analogy.  As  the  reader 
may  have  often  noticed,  the  same  class  of  minds  that 
are  satisfied  with  viewing  S  as  '  exactly  like '  ^,  will 
also  be  satisfied  on  occasion  (and  equally  through  ab- 
sence of  discriminative  power)  to  view  them  as  '  totally 
distinct.'  To  discriminate  is  to  see  points  of  difference, 
not  merely  to  deny  at  large  all  resemblance  whatever. 
For  some  reason,  however,  the  argument  from  'indis- 
criminate difference '  has  obtained  for  itself  no  express 
recognition,  though  it  certainly  exists.  Possibly  this  is 
to  be  explained  by  the  greater  pleasure  which  the  view 
of  resemblance  gives,  and  thence  the  greater  frequency 
of  loose  analogy.  But  since  the  danger  here  is  essen- 
tially the  same  as  the  danger  of  Analogy, — namely  the 
absence  of  exact  discrimination, — there  seems  to  be 
nothing  further  to  say  about  it  as  a  special  kind  of 
argument.  The  remedy  is,  to  call  for  the  supposed  point 
of  essential  difference,  and  thus  to  raise  the  argument  to 
the  deductive  rank. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  247 

Next,  the  expression  '  essential  difference '  is  one  of 
those  which  have  passed  so  freely  into  popular  use  as  to 
be  often  employed  without  a  clear  apprehension  of  their 
meaning.  Essential  means  again  here,  essential  for  some 
purpose  understood.  And  the  purpose  of  essential  differ- 
ence always  is,  to  break  down  some  supposed  analogy, 
or  to  deny  that  S  rightly  deserves  some  name.  Hence 
it  is  chiefly  for  Disproof  that  Distinction  by  point  of 
difference  is  used. 

It  is  clear,  however,  that  any  point  of  difference,  essen- 
tial or  not,  so  long  as  it  is  thoroughgoing, — so  long,  that 
is,  as  S  and  ^  entirely  differ  in  regard  to  its  possession, 
one  (universally)  having  it  and  the  other  (universally) 
having  it  not, — is  sufficient  to  support  the  thesis  S  -"w  J|^. 
But  S  may  differ  from  ^  in  many  points,  and  yet  a  given 
analogy  between  them  hold  good.  The  whole  force  of 
this  argument,  when  used  in  Disproof  of  analogy  or  sign, 
depends  upon  the  question  whether  the  point  of  differ- 
ence (M)  is  essential  for  the  purpose  in  hand. 

Those  who  have  not  fully  grasped  the  meaning  and 
importance  of  the  doctrine  as  to  the  burden  of  proof, 
may  find  at  first  sight  a  difficulty  here.  Is  it  incumbent 
on  the  disputer  of  an  analogy  to  prove  that  the  difference 
(M)  is  essential,  or  must  the  believer  prove  the  essen- 
tiality of  the  resemblance  relied  upon  ?  The  simple 
answer  is,  that  whichever  asserts  essentiality,  whether  of 
resemblance  or  of  difference,  must  prove  it  or  else  be 
content  to  make  an  apparently  unfounded  assertion.  It 
is,  of  course,  possible  that  the  disputer  of  an  analogy 


248  FALLACIEa  [Part  n. 

may  commit  himself  so  far  as  to  say  boldly  that  the 
analogy  fails  essentially;  but  this  would  be  a  highly 
gratuitous — often  a  rash — proceeding  on  his  part.  He 
may  usefully  make  a  milder  assertion  about  it,  namely 
that  he  sees  a  point  of  difference  and  is  anxious  to  inquire 
whether  the  believer,  having  duly  taken  it  into  account, 
has  reason  to  suppose  it  unessential  In  that  case,  of 
course,  he  avoids  all  burden  of  proving  anything  but 
simple  difference,  leaving  it  to  the  other  side  to  show 
wherein  essentiality  consists.  If,  however, — as  it  is 
sometimes  safe  to  do, — he  risks  the  full  assertion  that 
the  given  analogy  does  fail  essentially,  let  us  see  what 
it  becomes  incumbent  on  him  to  prove.  The  analogical 
argument  attacked  is,  say  : — 

S— >Z:  for  5b —^Z: 
But,  says  the  objector,  "  ^  — >  M,  while  S  — >  non-M, 
and  M  is  essential."  He  asserts  then  that  it  is  only 
because  ^  — >  M  that  ^  — >  Z ;  that  where  M  is 
absent  the  supposed  indication  of  Z  is  worthless.  This 
assertion,  therefore,  is  implied  in  calling  the  difference 
essential,  and  must  be  proved,  like  any  other  assertion, 
before  the  case  is  made  out. 

From  these  considerations  it  follows  that  Distinction 
by  Essential  Difference  can  never  be  used  except  in 
Disproof,  since  the  '  essential '  always  refers  to  some- 
thing gone  before.  And  it  is  also  clear  that  Distinction 
by  Simple  Difference  can  rarely  be  used  except  with 
reference  to  some  supposed  mistake,  since  the  positive 
assertion  contained  in  saying  merely  that  two  things 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  249 

differ  is  so  safe  as  to  be  practically  trivial.  Everything 
<liffers  from  everything  else  in  some  points, — even  a  coin 
from  its  neighbour  struck  the  next  moment  from  the 
Mint, — just  as  everything  also  resembles  in  some  point 
(even  if  it  be  only  in  being  'nameable')  every  other 
thing.  The  real  value  of  a  given  assertion  of  difference 
is  to  contradict  some  supposed  exaggeration  of  the  im- 
portance due  to  a  superficial  or  '  striking '  likeness. 

(c)  Exceptive  Disproof. 

That  the  exception  proves  the  rule,  has  passed  into 
a  popular  saying.  It  is  by  seeing  exceptions,  and  thus 
guarding  our  statements,  that  we  establish  any  law  on 
a  firm  basis,  making  it  henceforward  unexceptionable. 
By  searching  for  exceptions  we  test,  or  try,  the  law  set 
up  for  Proof  I  am  aware  that  this  much-abused  pro- 
verb is  also  sometimes  interpreted  to  mean  that  since 
the  given  fact  deserves  to  be  called  an  exception  it  must* 
be  comparatively  rare ;  but  such  an  employment  of  the 
phrase  (apart  from  its  etymological  shortcomings)  borders 
so  nearly  on  the  Petitio  principii — having  no  practical 
value  except  as  a  somewhat  epigrammatic  argumentum 
ad  hominem,  and  being  often  in  fact  employed  for  a 
very  different  purpose — that  it  seems  best  to  keep  in 
view  the  other  and  more  fruitful  meaning,  A  supposed 
law  which  is  found  false  in  one  instance  becomes  thereby 
fallible  in  all,  until  the  exceptions  are  incorporated  into 
its  statement  and  thus  its  application  narrowed.     Hence 


250  FALLACIES.  [Pabt  IL 

Disproof  by  exception  is  one  of  the  most  important 
processes  of  verifying,  and  so  establishing  or  discarding, 
our  theories.  The  '  best  explanation,'  or  '  proved  theory,' 
is  that  which  remains  over  as  a  residue  when  all  possible 
holes  have  been  picked  in  the  crude  or  sweeping  assertion 
first  put  forward  as  a  guess. 

Exceptive  Disproof  is  therefore  the  most  frequent 
mode  of  attacking  a  generalisation  directly:  attacking, 
that  is,  the  law  itself  asserted,  not  its  grounds.  To 
attack  its  grounds,  as  will  be  shown  presently,  the 
best  way  is  either  to  point  out  essential  difference  be- 
tween the  cases  observed  and  those  inferred,  or  else  to 
point  out  simple  diflference  and  inquire  whether  or  no  it 
is  known,  or  why  it  is  judged,  to  be  unessential.  But 
exceptive  disproof  finds  at  once  the  contradictory  instance. 

Amongst  the  misleading  statements  that  float  about 
so  freely  in  common  parlance  is  one  to  the  effect  that 
"  Nothing  is  so  hard  as  to  prove  a  negative."  The  re- 
verse is  the  actual  case.  Disproof,  qud  Disproof,  is  safer 
and  easier  than  Proof,  just  as  destruction  is  less  trouble- 
some than  construction.  In  Disproof,  since  the  Thesis 
is  a  bare  denial,  we  commit  ourselves  to  the  least 
possible  amount  of  dogmatic  statement.  We  merely 
assert  that  some  other  given  proposition  is  false,  with- 
out venturing  to  say  exactly  what  is  true  in  place  of 
it.  The  fact  that  underlies,  and  (with  proper  explana- 
tion) may  be  held  to  justify,  the  popular  expression 
above  quoted,  is  mainly  the  difficulty  that  attaches  to 
such    far-reaching    words    as    'never,'    'nowhere,'  'no 


Chap.  VL]      THE   EMPLOYMENT  OF  GUESSWORK.  251 

one,'  and  the  like.  '  Positive '  assertions,  whose  cor- 
responding negatives  are  obliged  to  employ  these 
words,  are,  through  their  vagueness,  so  securely  guarded 
against  being  brought  to  an  actual  test,  that  Dis- 
proof often  becomes  practically  impossible.  To  prove, 
e.g.  that  my  neighbour  has  never  been  in  New  York,  or 
that  no  one  has  ever  held  a  certain  opinion,  is  of  course 
to  disprove  the  very  vague  assertion  that  these  events 
iniay  (at  some  time  or  other)  have  happened, — an  asser- 
tion with  which  it  is  commonly  safer,  and  perfectly 
harmless,  to  agree.  Again,  Disproof  is  sometimes  as 
diflBcult  as  Proof — not  more  so.  To  disprove  the  exist- 
ence of  Buddha,  or  of  table-rapping  spirits,  is  manifestly 
impossible  so  long  as  there  is  no  admitted  test  to  which 
the  question  can  be  brought.  But,  as  De  Morgan  has 
remarked,  whenever  we  set  out  to  prove  (in  the  narrower 
sense)  any  Thesis,  we  must  be  prepared  to  dispi^ove  any 
one  or  more  of  an  indefinite  number  of  other  assertions 
that  conflict  with  it;  while  in  order  to  disprove  any 
Thesis  we  need  only  reduce  it  to  absurdity ;  which  is 
often  possible  without  our  being  prepared  to  prove  a 
single  positive  assertion  about  the  matter.  A  definite 
theory,  whether  abstract  or  concrete,  can  be  disproved 
by  '  experience  '  more  easily  than  it  can  be  proved :  for 
in  disproof  we  have  only  to  find  some  single  instance 
which  conflicts  with  the  assertion  if  abstract,  some  single 
point  in  which  it  fails  if  concrete.  It  is  in  fact  mainly 
by  means  of  this  simpler  disproving  operation  that  the 
securest  experimental  Proof  takes  place.    All  testing  of 


262  FALLACIES.  [Past  II, 

a  Theory  set  up  is,  at  bottom,  nothing  else  than  a  search 
for  contradicting  facts  existing  or  inferrible.  On  the 
thoroughness  of  the  search  the  value  of  the  test  depends. 
After  a  long  life  of  honourable  security  any  theory  may 
be  in  a  moment  upset,  or  at  least  may  be  found  to  need 
qualification,  by  the  discovery  of  a  single  hidden  circum- 
stance :  and  experimental  inquiry  in  its  highest  form  is 
in  reality  an  attempt  to  dispose  beforehand  of  all  rele- 
vant facts  that  can  by  any  means  be  brought  to  light. 

As  regards  the  two  varieties  of  this  form  of  argument, 
(given  on  p.  242)  not  much  requires  to  be  said.  The  use 
of  the  one  or  the  other  clearly  depends  on  the  nature  of 
our  previous  knowledge  bearing  on  the  question  raised. 
Neither  mode  can,  I  think,  be  called  altogether  safer  or 
better  than  the  other,  since  even  direct  identification  of 
M  with  S  may  well  be  mistaken.  If,  however,  any  pre- 
ference is  to  be  given,  perhaps  the  latter  (BoJcardo)  should 
have  it.  The  dangers  in  the  way  of  these,  as  of  all  forms 
of  deductive  argument,  will  be  treated  in  a  later  section. 

III.  The  Dangers  of  the  Argument  by  Example.* 

(a)  Tlie  Dangers  of  Analogy. 

In  both  kinds  of  Argument  by  Example, — Analogical 
reasoning  and  Inductive  Proof — the  primary  danger  is 
that  of  overlooking  some  hidden  element  in  the  facts, 
and  thereby  generalising  too  freely,  rather  than  that 

*  The  dangers  peculiar  to  the  special  types  of  argument  are  shown, 
all  together,  in  a  table  (V.)  in  the  Appendix  (E). 


Chap.  VI.]      THE  EMPLOYMENT  OF  GUESSWORK.  253 

of  accepting  a  definite  principle  which,  true  or  not, 
does  not  apply.  We  are  not  here  concerned  with  any 
dangers  to  argument  when  the  principle  relied  upon  is 
simple  and  clear,  but  solely  with  those  incident  to  rapid 
unconscious  employment  of  some  highly  complicated 
principle,  or  to  our  hurried  summary  of  the  total  outcome 
of  a  conflict  between  unnumbered  dimly  formulated  laws. 

It  was  said  above  that  in  adopting  Mill's  formula  for 
Analogy  as  typical,  we  must  bear  in  mind  that  an  actual 
argument,  though  truly  analogical,  may  easily  appear  on 
the  surface  not  quite  to  fit  the  formula.  But  this  formula 
is  nevertheless  a  perfectly  legitimate  simplification,  since 
it  serves  to  generalise  the  one  danger  to  which  all  analo- 
gical arguments,  in  so  far  as  analogical,  are  primarily 
liable  :  the  danger,  namely,  that  the  resemblance  between 
the  cases  supposed  to  be  analogous  is  only  a  superficial 
one, — or,  more  widely  still,  that  the  resemblance,  even 
if  on  the  whole  real  and  deep,  is  not  essential  for  the 
purpose  intended.  So  far  as  an  argument  professes  to 
rest  on  analogy,  the  matter  of  first  importance  is  to  ascer- 
tain, if  possible,  the  exact  points  of  resemblance  and 
difference  between  the  cases  compared,  and  to  inquire 
further  whether  the  resemblance  as  thus  defined  and 
limited  has  any  right  to  be  considered  essential  in  regard 
to  the  purpose  for  which  it  is  in  the  given  case  employed. 

We  saw  also  that  the  real  difficulty  in  clearly  placing 
the  argument  from  Analogy  among  special  kinds  of 
Proof,  arises  from  the  fact  that  as  soon  as  the  exact 
points  of  resemblance  relied  upon  come  into  clear  view 


254t  FALLACIES.  [Part  H. 

the  argument  ceases  to  be  analogical,  and  becomes  deduc- 
tive. That  is  to  say,  if  we  rest  our  belief  that  S  — >  Z 
on  the  observed  fact  that  ^  (which  resembles  S  in  the 
point  M)  — >  Z,  we  are  really  beginning  to  employ, 
instead  of  mere  analogy,  the  fuU  syllogism  '  S  — >  Z,  for 
S  — >  M,  and  M  *  — >  Z.'  Our  clear  recognition,  that 
is,  of  the  exact  extent  of  resemblance  relied  upon,  is 
itself  a  recognition  of  the  underlying  Principle  by  virtue 
of  which  S  and  ^  are  considered  '  parallel  cases ; '  in 
other  words,  is  an  assumption  of  a  Law  from  which  our 
thesis  may  be  deduced.  Take,  for  instance,  the  argument 
sometimes  employed  against  Sunday  closing,  that  since 
the  upper  classes  have  their  clubs  open  on  that  day  it 
would  be  unfair  to  deprive  the  poor  of  their  only  places 
of  resort  and  refreshment.  It  is  clear  at  once  that  we 
have  here  a  case  of  complicated  or  double  analogy,  clubs 
being  considered  to  '  essentially  resemble '  public-houses, 
and  the  upper  classes  to  essentially  resemble  the  lower. 
But  what  is  meant  by  '  essential  resemblance  ? '  Not, 
surely,  that  the  things  compared  are  precisely  alike  in  aU 
respects, — else  detection  of  false  analogy  would  be  a  far 
simpler  matter  than  at  present  but  that  for  the  purposes 
immediately  in  view,  the  points  of  difference  may  be 
neglected.  Now,  as  soon  as  we  begin  to  neglect  points  of 
difference,  no  matter  where,  we  begin  to  generalise :  that 
is  to  say,  we  extend  the  possible  range  of  our  assertion. 
That  which  constitutes  individuality  is  always  the 
difference  {i.e.  peculiarity)  that  an  individual  possesses 

*  If  not  rmirersallj,  at  any  rate  eqnally  when  limited  by  S  and  Sb. 


CuAP.  Vl]      THE  EMPLOYMENT  OF  GUESSWORK.  255 

over  and  above  any  class  to  which  he  may  belong, 
just  as  we  have  seen*  that  it  is  differentia  that 
the  sub-class  or  species  possesses  over  and  above  the 
genua.  So  far,  then,  as  we  neglect  the  points  of  difference 
between  clubs  and  public-houses,  or  between  one  class  of 
men  and  another,  we  speak  of  them  no  longer  as  distinct 
individual  things,  but  as  members  of  some  wider  class . 
which  includes  them  and  may  possibly  include  other 
things  as  well.  In  the  instance  quoted,  the  key  to  the 
class  intended  is  expressly  given  in  the  case  of  the 
analogy  between  clubs  and  public-houses :  it  is  the  being 
places  of  'resort  and  refreshment'  that  is  considered 
essential :  this  is  the  point  of  resemblance  in  virtue  of 
which  (i.e.  to  the  extent  of  which)  what  is  true  of  the 
one  is  supposed  to  be  true  of  the  other.  As  regards  the 
analogy  between  upper  and  lower  classes,  it  seems  to 
have  been  thought  unnecessary,  or  unsafe,  to  give  the 
key  expressly;  such  maxims  as  that  "no  class  in  the 
State  should  be  specially  favoured  without  reason  shown  " 
being  widely  accepted  as  a  basis  of  legislation.  And  if 
this  account  of  the  analogy  intended  be  a  correct  one, — 
if  it  is  only  as  being  places  of  resort  and  refreshment 
that  public-houses  are  to  be  kept  open  for  the  benefit  of 
the  poor  in  their  sole  capacity  of  citizens  of  the  State 
(or  whatever  may  be  the  wide  class  to  which  upper  and 
lower  classes  equally  belong) — then  we  thereby  imply 
the  Generalisation,  or  Law,  or  Principle,  "All  citizens 
of  the  State  are  (a  pHori)  equally  entitled  to  their 

*  Cf.  p.  108,  above. 


256  FALLACIES.  [Pabt  II. 

places  of  resort  and  refreshment ; "  by  means  of  which,  if 
true,  the  Thesis  may  be  deductively  proved. 

However  important,  therefore,  Analogy  may  be  as 
setting  us  on  the  track  of  a  fruitful  Inference,  as  a  mode 
of  Proof  it  is  in  itself  almost  wholly  worthless, — only 
sufficient,  that  is,  to  raise  a  vague  and  slight  presumption 
where  no  better  evidence  can  be  obtained.  It  is  perhaps 
more  widely  applied,  in  common  discourse,  even  for 
Proof  as  well  as  for  Inference,  than  any  other  form  of 
argument.  But  this  seems  to  be  chiefly  due  to  the  slack- 
ness with  which  our  examination  of  evidence  is  commonly 
carried  on.  It  is  so  much  less  trouble  to  see  that  two 
things  bear  a  '  striking  resemblance '  than  to  discriminate 
accurately  how  far  the  resemblance  really  goes,  and  the 
points  wherein  they  differ.  There  is  nothing,  pro- 
bably, that  is  more  characteristic  of  the  higher*  in- 
tellect as  contrasted  with  the  lower  than  its  greater 
power  of  discriminating, — i.e.  of  seeing  points  of  diflfer- 
ence.  It  is  differentiation  that  is  always  the  law  of 
progress.  Knowledge  begins  as  a  vague  blur,  which 
gradually  becomes  distinct  Everywhere  the  specialist's 
eye  sees  finer  shades  of  difference  than  are  visible  to  the 
public, — as  the  shepherd  knows  his  sheep.  It  is  incapa- 
city for  seeing  difference  that  lies  at  the  root  of  all  crude, 
ill-considered  generalisation,  and  therefore  at  the  root  of 
the  mental  *  narrowness '  (as  it  is  usually  called)  which  is 

*  Cf.  H.  Spencer,  Fgychology,  p.  220.  "  Incident  forces  that  seem 
alike  to  a  lowly  endowed  creature,  seem  conspicuously  unlike  to  a  crea- 
ture endowed  with  the  sense-organs  required  for  appreciating  them." 


Chap.  VI.]      THE   EMPLOYMENT  OF  GUESSWORK.  257 

ever  ready  to  accept  a  principle  unduly  simple  and  wide 
in  its  asserted  sweep,  and  therefore  unduly  rigid  in  its 
actual  application.  It  is  neglect  of  difference  that  always 
marks  the  ruder  nature,  easily  content  with  the  roughest 
weights  and  measures.  It  is  the  besetting  danger  not 
only  of  ignorance  as  opposed  to  experience,  of  clumsiness 
as  opposed  to  delicacy  of  touch,  but  also  of  the  habit 
of  dreamy  theorising  as  opposed  to  patient  reverence  for 
fact 

In  thus  noticing  the  harm  of  neglecting  difference,  I 
must  not  be  understood,  of  course,  to  advocate  the  neg- 
lect of  real  resemblance ;  only  to  say  that  this  is  a  fault 
to  which  the  majority  are  in  practice  far  less  liable.  The 
inducements  to  over-generalise  are  on  the  whole  stronger 
than  those  to  indulge  in  excessive  hair-splitting.  And 
apart  from  mere  ignorance  or  incapacity,  it  is  always  less 
trouble  to  avoid  distinguishing,  even  when  we  have 
attained  the  power:  the  recognition  of  resemblance, 
whether  justified  or  not,  is  always  a  more  pleasant 
operation,  simplifying  Nature  and  thereby  giving  freedom, 
and  also  much  self-satisfaction,  to  the  mind  that  sees  the 
supposed  analogy.  Hence,  no  doubt,  much  of  the  charm 
of  metaphor  and  of  the  cruder  kinds  of  poetry,  and 
hence  the  efficacy,  in  spite  of  its  unfairness,  of  caricature. 
Whatever  appeals  to  our  idleness,  while  at  the  same  time 
gently  flattering  our  sense  of  '  breadth  of  view/  always 
bids  fair  to  win  a  wide  reception.  In  its  effects,  hair- 
splitting is  perhaps  a  more  deadly  fault  than  coarseness 
of  vision,  though  less  the  property  of  the  uninstructed,  the 


258  FALLACIES.  [Part  II. 

thoughtless,  the  impatient,  and  the  clumsy.  The  power 
of  seeing  differences,  exclusively  cultivated,  leads  no  doubt 
to  a  casuistry  and  a  hesitation  which  are  far  from  being 
either  pleasant  or  practical.  So,  too,  the  mere  neglect  of 
resemblance,  without  at  the  same  time  a  distinct  and 
conscious  vision  of  differences,  cripples  our  power  of  ex- 
tended sight  and  of  useful  generalisation.  This  forms 
indeed  no  fallacy ,  as  the  term  is  generally  understood ; 
but  it  is  a  serious  limitation,  as  the  existence  and  spread 
of  general  names,  and  of  science  itself,  bears  standing 
witness.  Often,  no  doubt,  it  is  merely  the  recoil  from 
hasty  generalisation  that  leads  to  the  adoption  of  '  rule 
of  thumb : '  in  any  case,  however,  this  is  of  course  a 
falling  short  from  the  ideal. 

It  is  the  undue  neglect  of  difference,  then,  in  the  midst 
of  recognised  resemblance,  that  constitutes  the  fallacy  of 
False  Analogy,  just  as  the  due  neglect  of  difference  con- 
stitutes sound  generalisation.  While  the  ideal  is,  to  give 
to  both  Resemblance  and  Difference  their  due  weight,  the 
actual  course  of  the  history  of  knowledge,  so  far  back  as 
it  can  be  traced,  is  a  record  mainly  of  unsuspected  dif- 
ferences brought  to  light.  Where  any  sound  generalisa- 
tion has  been  reached,  it  has  in  most  cases  either  been 
preceded  by  deep  analysis,  or  is  itself  the  residue  of  an 
unsound  generalisation  after  it  has  gone  through  a  pro- 
cess of  limitation  and  restriction  in  order  to  make  it  fit 
the  facts.  Further  back  than  any  records  go.  Philology 
helps  us  to  see  that  the  earliest  traceable  formation  of 
language  has  proceeded  also  by  analysis  of  what  first 


Chap.  VI.]   THE  EMPLOYMENT  OF  GUESSWORK.        259 

seemed  simple.  First  we  find  one  word  employed  for 
what  we  now  know  to  be  many  different  things  :  gradu- 
ally, as  insight  deepens,  new  words  grow  up,  in  order  to 
mark  off  groups  and  portions  as  distinct.  While  there 
may  be  a  synthesis  based  upon  analysis,  the  first  step  is 
to  analyse  what  before  seemed  simple. 

The  shapes  in  which  False  Analogy  usually  occurs  are 
very  numerous.  They  range  from  open  reliance  on 
Analogy  in  lieu  of  Proof,  down  to  the  finest  shades  of 
rhetorical  suggestion  by  means  of  metaphor ;  and  even 
into  the  region  where  metaphor  ceases  to  be  distinguish- 
able as  such,  and  where  we  reach  the  unavoidable  short- 
comings of  language.  Taking  first  the  more  definite  end 
of  the  scale,  the  following  example  will  show  to  some 
extent  the  dangers  of  analogy.  An  eminent  author, 
writing  on  the  work  of  the  English  Church  before  the 
Tractarian  movement,  contrasts  the  newer  state  of  things 
unfavourably  with  the  older,  because  the  Church  in  those 
former  days 

"taught  us  to  use  religion  as  a  light  by  which  to  see  our  way 
along  the  road  of  duty.  Without  the  Sun  our  eyes  would  be  of  no  use 
to  us ;  but  if  we  look  at  the  Sun  we  are  simply  dazzled  and  can  see 
neither  it  nor  anything  else.  It  is  precisely  the  same  with  theological 
speculations.  If  the  beacon  lamp  is  shining  a  man  of  healthy  mind 
will  not  discuss  the  composition  of  the  flame." 

Here,  of  course,  the  resemblance  between  the  Pro- 
testant religion  and  a  light  to  lighten  the  road  of 
duty  is  sufficiently  striking,  and  (if  it  be  granted,  as 
for  the   purpose   of  this   argument  it   may   safely  be. 


260  FALLACIES.  [Part  II. 

that  the  light  is  no  mere  will-of-the-wisp)  no  fault 
need  be  found  with  the  metaphor  so  far.  But  in  what 
respects  do  '  theological  speculations '  really  resemble 
the  process  of  '  looking  at  the  light '  ?  Whatever 
other  faults  the  movement  spoken  of  may  have  had, 
surely  it  was,  in  essentials,  an  attempt  to  look  more 
closely  at  the  road  of  duty  as  illumined  hy  the  light.  To 
call  this  looking  at  the  light  is  merely  a  loose  and  con- 
venient elliptical  expression.  At  any  rate,  nothing  is 
openly  said  by  the  writer  to  show  that  this  latter 
employment  of  the  metaphor  is  not  a  better  one,  and  if 
we  are  to  suppose  such  a  denial  covertly  made,  it  comes 
very  near  to  begging  the  most  important  question  con- 
cerned. But  in  order  to  show  more  strikingly  the 
worthless  character  of  analogy  as  argument,  it  may  be 
further  noticed  that  in  the  second  half  of  the  sentence 
the  metaphor  is  changed,  by  its  author  himself,  in  a  way 
that  saves  an  opponent  all  trouble,  inasmuch  as  it  forces 
the  first  analogy  to  defeat  its  own  purpose.  Religion 
becomes  no  longer  a  Sun  for  lighting  up  the  road,  but 
a  'beacon  lamp,' — a  thing  whose  use  and  purpose  is 
precisely  to  be  looked  at :  and  in  order  to  save  the  argu- 
ment, theological  speculation  has  now  to  be  likened  to 
'discussing  the  composition  of  the  flame.'  Would  not 
the  Tractarians  say  rather  that  if  they  cared  to  discuss 
the  composition  of  the  flame  at  all,  it  was  only  so  far  as 
might  enable  them  to  be  sure  that  this  really  was  the 
*  beacon  lamp  '  of  which  they  were  in  search  ?  Analogy 
used  in  this  way  is,  no  doubt,  as  things  are,  a  powerful 


Chap.  VI.]      THE  EMPLOYMENT  OF  GUESSWORK.  261 

rhetorical  instrument ;  but  it  is  not  one  that  is  destined 
to  extend  its  influence  in  the  future.  The  remedy  is  so 
easy.  Give  a  dealer  in  analogy  rope  enough  and  he  will 
probably  end  as  above ;  but  if  not,  and  if  it  be  considered 
too  much  trouble,  or  too  difficult,  or  too  slow,  to  inquire 
exactly  into  the  real  points  of  resemblance  and  difference, 
nothing  is  simpler  than  to  change  the  metaphor  and  so  turn 
the  tables.  One  arguer  can  always  assert  covertly  as  well 
as  another,  and  it  requires  no  great  intellectual  strain  to 
produce  a  happy  simile  or  to  fix  the  attention  of  a  busy 
or  thoughtless  audience  on  some  '  striking  likeness '  which 
is  so  neat  and  pretty  that  it  seems  to  them  it  cannot 
be  untrue.  It  is,  however,  solely  when  a  supposed 
analogy  is  put  (or  accepted)  in  place  of  argument  that 
harm  is  done.  As  mere  illustration,  or  as  re-assertion 
of  a  thesis  in  a  more  concrete  form,  only  pedantry  can 
object  to  it ;  and  as  supplying  the  first  vague  hints  for 
future  verification  it  will  always  be  the  chief  stepping- 
stone  to  good  results.  But  the  line  between  employing 
Analogy  as  argument  and  employing  it  with  an  open 
recognition  of  its  dangers  is  so  exceedingly  fine  that  it 
becomes  in  practice  almost  impossible  to  over-estimate  the 
need  of  keeping  a  jealous  guard  against  neglected  points 
of  difierence.  It  must  also  be  remarked,  that  even  where 
the  analogy  is  plainly  a  false  one,  it  is  always  possible 
that  the  person  employing  it  has  himself  been  under  no 
delusion  as  to  the  gap  requiring  to  be  filled  up,  but  has 
only  overrated  the  discriminative  power  of  his  audience, 
— or  forgotten  their  readiness  to  be  deceived. 


262  FALLACIES.  [Pabt  IL 

Open  reliance  on  Analogy  as  argument  is  rare.  The 
analogical  arguments  that  we  find  actually  employed 
show  a  decided  disinclination  to  express  themselves  in  a 
quite  straightforward  fashion ;  unless,  indeed,  as  in  some 
of  the  cases  above  quoted,  the  connecting  link  (or  middle 
term)  is  fairly  obvious,  and  the  argument,  therefore, 
already  nearly  deductive  and  easily  raised  to  that  higher 
rank.  As  a  general  rule,  the  more  merely  analogical  {i.e. 
the  less  deductive)  the  argument  is,  the  more  will  it 
naturally  tend  to  avoid  open  and  definite  expression  by 
means  of  this  simplest  formula :  for  the  definite  expres- 
sion of  reliance  upon  the  resemblance  between  S  and  ^ 
to  prove  a  definite  assertion  regarding  S,  is  apt  to  pave 
the  way  for  inquiries  that  are  then  felt  to  be  awkward. 
When  the  Analogy  is  a  weak  one  (and  equally  when  the 
points  of  resemblance  are  numerous  or  not  easily 
summed  up)  nothing  of  course  is  more  damping  to  the 
argument  than  any  call  for  a  clear  statement  of  the  exact 
points  of  resemblance  relied  upon ;  and  hence  in  many 
cases  even  the  setting  S  and  ^  clearly  side  by  side,  and 
reducing  the  reasoning  to  the  above  formula,  becomes 
almost  tantamount  to  a  reduction  of  the  whole  argument 
to  absurdity ;  and  is  constantly  employed  for  that  purpose. 
Thus  when  a  speaker  in  Parliament  declared  that — 

"To  say  that  there  was  nothing  in  the  nature  of  a  compact  or 
agreement  between  the  Government  and  the  gentlemen  whom  they 
had  been  keeping  in  confinement  without  trial,  reminded  him  of  the 
principal  character  in  one  of  Moliere's  comedies,  who  said  that  he  had 
not  sold  anything,  but  had  merely  given  it  away  to  his  friends  and 
they  had  given  him  some  money  in  exchange —  " 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  263 

we  find  the  other  side  making  answer  that — 

"  So  far  as  the  speech  of  the  hon.  member  was  not  a  mere  baseless 
dream  ...  it  contains  at  least  this  one  statement,  that  because  in 
Molierc  there  was  a  man  who,  having  sold  goods  and  received  a  price, 
pretended  that  he  had  made  a  present  of  the  goods  and  received  a  pre- 
sent in  return,  the  position  of  the  Government  is  analogous  to  that 
man." 

And  then  comes  a  statement  of  the  "  essential  differ- 
ence "  between  the  two  apparently  parallel  cases. 

As  a  general  rule,  then.  Analogy  has  a  tendency  in 
practice  to  put  itself  forward  either  as  merely  intended 
to  raise  a  vague  presumption,  or  else  (and  more  com- 
monly), with  an  air  of  coming  ex  ahundanti,  rather  than 
as  being  in  fact  the  sole  evidence  relied  upon.  It  is 
usually  given,  however  unintentionally,  in  such  a  manner 
that,  if  objections  should  be  raised,  it  remains  easy  to 
claim  that  only  an  illustration  was  intended,  and  to  grant 
with  much  candour  that  possibly  as  an  illustration  it 
fails  to  fit  the  case  exactly;  a  process  which  closely 
resembles  the  parliamentary  practice  of  first  using  and 
then  '  withdrawing '  an  offensive  expression.  The  express 
words  'because,'  or  'for,*  or  'since/  are  as  a  rule 
omitted  by  the  speaker:  the  connexion  will  be  amply 
supplied,  as  every  experienced  rhetorician  must  know,  by 
any  average  audience,  and  being  thus  voluntarily  supplied 
by  the  audience,  will  probably  be  less  exposed  to  their 
criticism.  Whately,  for  example,  did  not  write,  "In- 
ductive Logic  can  never  be  a  rival  to  the  Aiistotelian 
Logic,  since  a  plough  can  never  be  substituted  for  a  flail," 
but  he  wrote  that  Inductive  Logic — 


264  FALLACIES.  [Pabt  U. 

"  Would  not  .  .  ,  have  the  same  object  proposed  with  the  Aristo- 
telian Logic  ;  nor  be  in  any  respect  a  rival  to  that  system.  A  plough 
may  be  a  much  more  ingenious  and  valuable  instrument  than  a  flail, 
but  it  can  never  be  substituted  for  it."  * 

Or  again,  Sir  S.  Northcote  (speaking  at  Balham), 
did  not  say  "Mr.  Gladstone,  hecause  he  is  fond  of 
hewing  down  trees,  will  be  likely  to  want  to  hew  down 
our  institutions,"  but  he  said — 

"  We  shall  be  abused  by  a  great  number  of  people  because  we 
hesitate  to  give  to  the  Prime  Minister  exactly  the  facilities  he  de- 
mands, but  we  shall  endeavour  to  do  our  duty  when  those  demands 
are  made  upon  us ;  and  we  may  take  to  heart  one  of  those  wise  fables 
on  which  our  youth  was  nourished.  You  may  remember  how  a  cer- 
tain woodman  went  into  the  forest  and. asked  the  trees  to  lend  him  a 
bit  of  wood  in  order  that  he  might  make  a  handle  to  his  axe.  When 
they  were  unwise  enough  to  give  him  a  piece  of  wood,  you  recollect 
what  happened  to  the  trees  themselves  by  the  use  the  woodman  made 
of  the  axe  (cheers  and  laughter)."  • 

These  examples  will  be  suflScient  to  show  what  is  here 

intended.     But  the  difficulty  of   deciding  whether  the 

Analogy  was  really  relied  upon  as  evidence,  or  genuinely 

and  legitimately  put  forward  as  an  illustration  merely, 

or  to  point  a  quaint  and  semi-serious  fancy,  is  not  the 

only  one  to  which  we  are  exposed  in  practice,  nor  the 

most  perplexing.     This  can,  indeed,  to  a  great  extent  be 

met  (much  as  an  unparliamentary  expression  may  be 

met)  by  demanding  a  disclaimer  on  the  spot.    A  far  more 

difficult  question  arises  when  we  attempt  to  fix  the  line 

between  the  metaphorical  and  the  direct  use  of  Tianies 

*  The  reader  will  notice  that  these  cases  are  not  given  as  examples 
of  false  analogy,  bat  merely  of  the  usual  method  of  getting  an  analogy 
(true  or  false)  accepted  by  an  audience. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  265 

And  perhaps  the  most  frequent  manner  in  which  covert 
analogy  is  used  as  argument,  is  by  condensation  into  a 
name  which  just  escapes  being  considered  far-fetched  or 
metaphorical. 

"  It  was  observed  by  a  sound  thinker  in  those  parts,  that  property 
was  ballast,  and  when  once  the  aptness  of  that  metaphor  had  been 
perceived,  it  followed  that  a  man  was  not  fit  to  navigate  the  sea  of 
politics  without  a  great  deal  of  such  ballast." 

That  which  to  George  Eliot  and  to  most  of  her  readers 
was  clearly  a  mere  metaphor,  the  aptness  of  which 
was  all-important  to  the  force  of  the  argument,  passed 
easily,  she  tells  us,  among  the  less  educated  electors 
of  Treby  Magna,  as  hardly  distinguishable  from  a  plain 
statement  of  fact.  The  power  of  recognising  metaphor 
as  metaphor  is  one  of  the  latest  and  highest  acquisitions 
(so  far  as  it  is  yet  acquired)  of  mankind ;  an  outgrowth 
of  the  accurate  spirit  which  marks  off  modern  science 
from  the  ancient  reign  of  florid  imagination. 

To  some  extent,  however,  we  are  all  in  the  position  of 
these  electors.  We  smile  at  their  simplicity,  but  future 
generations  will  smile  at  ours  in  turn.  The  schoolboy 
of  the  twentieth  century  may  find  a  difficulty  in  realising 
that  his  ancestors  were  misled  into  supposing  fleshiness 
of  body  to  be  "  padding  against  the  shafts  of  disease," 
or  a  glass  of  sherry  taken  just  after  a  large  and  varied 
dinner,  to  be,  in  the  sense  intended,  a  "whitewash," 
At  present  the  words  are  few  where  metaphor  is  wholly 
absent,  and  under  metaphor  wherever  employed  some 
danger  lurks.     Who  is  to  guarantee,  for  example,  that 


266  FALLACIES.  [Paet  U. 

the  expression  that  danger  "lurks"  in  metaphor  will 
not  at  all  mislead  us  ?  We  are  always  rather  prone  to 
personify  abstractions,  and  so  far  as  we  really  picture 
Fallacy  as  external  to  ourselves,  we  are  neglecting  one 
of  the  most  important  facts  about  it. 

Proverbs  again  are  frequently  employed  in  arguing  by 
indistinct  resemblance.  It  is  the  slackness  with  which 
any  '  striking '  analogy  will  commonly  pass  muster  that 
leads  at  all  times  to  the  use  so  freely  made  of  proverbs. 
To  a,ssume  that  some  case  comes  under  some  well-known 
proverb,  without  a  shadow  of  evidence  to  show  that  it 
does  so  beyond  what  may  be  gathered  from  the  crudest 
superficial  inspection,  is  still  in  many  quarters  a  favourite 
practice.  Hence,  as  a  rule,  the  earliest  recorded  crys- 
tallisation of  wisdom  has  usually  been  a  collection  of 
proverbs  or  of  fables  or  allegories, — which  latter  are 
only  a  less  generalised  form  of  the  same  expedient, — and 
to  some  extent  the  process  appears  to  be  still  going  on. 
It  is  true  that  in  these  times  such  oracular  wisdom 
obtains  less  influence  than  in  the  days  of  Solomon  or 
even  of  Bacon,  but  one  must  admit  that  there  is  still 
some  chance  for  a  writer  to  win  in  this  way  a  certain 
popular  reputation  for  prophetic  insight.  On  aU  such 
easy  dogmatism  the  action  of  Logic  is  apt  to  be  purely 
repressive. 

We  see  then,  in  short,  that  analogical  reasoning  may 
be  defined  as  the  dim  and  unsupported  assertion  of 
essential  resemblance.  To  assert  essential  resemblance 
is  in  itself  a  large  undertaking,  and  yet  there  are  few 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  267 

assertions  which  are  commonly  made  with  a  lighter 
heart  or  believed  more  obstinately.  Only  before  the 
resemblance  between  S  and  ^  is  clearly  defined  and 
limited,  can  an  argument  be  properly  called  analogical : 
and  meeting  with  an  argument  which  is  at  present  in  the 
merely  analogical  stage,  the  first  step  towards  its  exami- 
nation is  the  attempt  to  clearly  define  and  limit  the 
extent  of  the  resemblance  and  difference  supposed  to 
exist :  which  attempt,  so  far  as  successful,  destroys  the 
merely  analogical  character  of  the  argument,  by  bring- 
ing into  daylight  the  supposed  underlying  Principle. 
The  special  danger  of  any  argument,  so  far  as  it  relies 
upon  Analogy,  is  the  possible  existence  of  unsuspected 
and  essential  difierence  between  the  things  compared. 
This  is  the  vital  point  of  every  analogical  argument,  the 
point  to  which  attack  should  be  directed,  and  which,  if 
we  are  defending  the  analogy,  it  behoves  us  most  to  be 
prepared  to  guard.  Until  this  doubt  is  set  at  rest,  there 
is  nothing  to  show  that  the  resemblance,  how  striking 
soever,  is  more  than  surface-deep,  or,  even  if  really  far- 
reaching,  that  it  has  any  bearing  upon  the  special  point 
at  issue. 

(b)  The  Dangers  of  Induction. 
Before  beginning  to  discuss  the  dangers  of  the  induc- 
tive mode  of  argument,  it  may  be  worth  while  to  recall 
attention  to  the  various  shades  of  assertion  comprised 
under  the  extremely  general  formula  S  — >  ^.  In  the 
first  place,  it  must  be  remembered  (as  noticed  at  pp.  78-83) 


268  FALLACIES.  [Paet  II. 

that  at  the  present  stage  of  knowledge  the  propositions 
where  such  a  statement  can  be  in  practice  interpreted 
quite  unreservedly  are  comparatively  few  in  number. 
Here  and  there,  certainly,  we  have  discovered  generalisa- 
tions which  seem  absolutely  true,  so  far  at  least  as  our  tests 
can  yet  try  them  and  so  far  as  all  present  practical  pur- 
poses are  concerned, — such  as  the  Law  of  Causation  itself, 
or  the  law  that  human  beings  have  human  ancestors, 
or  that  all  matter  gravitates,  or  that  decapitation  causes 
death.  But  for  the  most  part,  even  in  Science,  we  are 
forced  to  be  content  with  laws  which  express  tendencies  * 
merely.  Often,  indeed,  we  think  ourselves  fortunate  if 
we  can  reach  any  shadow  of  a  law  at  all.  It  is  no  ex- 
aggeration to  say  that  the  greater  part  of  the  knowledge 
on  which  daily  conduct  depends  for  its  rationalisation 
consists  solely  of  generalisations  which,  however  crudely 
and  boldly  expressed  and  at  intervals  believed,  are  really 
apprehended  (so  far  as  regards  persistent  or  fruitful 
apprehension)  in  the  dimmest  and  vaguest  way.  To  go 
no  further  than  the  popular  maxim  in  favour  of  speaking 
the  truth,  every  thoughtful  person  will  admit  nowadays 
that  the  law  as  usually  stated  needs  some  qualification ; 
although  most  people  feel  the  admission  dangerous,  since 
no  one  has  yet  been  able  to  formulate  the  real  law  so 
as,  while  avoiding  mere  platitude,  to  take  in  all  the 
exceptions. 

*  The  law  of  Gravity,  it  should  be  noticed,  merely  avoids  this  diffi- 
culty in  a  verbal  manner.  It  is  absolutely  true  that  all  matter  gravitates  : 
but  'gravitates'  is  a  word  coined  to  express  the  meaning  'tends  to 
faU.' 


Chap.  VI.]       THE   EMPLOYMENT  OF  GUESSWORK.  269 

Next,  S  (in  general)  may  be  asserted  to  indicate  ^ 
(whether  absolutely  or  reservedly)  either  as  its  cause,  its 
concomitant,  or  its  effect, — that  is,  either  as  having  ex-" 
isted,  as  existing,  or  as  to  exist  in  the  future.  To  assert 
that  ^  is  *  the  sole  cause  of  S  is  to  assert  absolutely  that 
S  wherever  found  indicates  ^'s  past  existence  {e.g.  '  Life 
is  always  due  to  prior  life ') :  to  assert  the  same  indica- 
tion '  reservedly '  is  to  assert  either  that  ^  is  one  cause 
but  that  there  may  be  others ;  or,  in  the  most  reserved 
form  of  all,  that  an  observed  sequence  ^  followed  by  S 
was  '  not  purely  accidental.'  f  To  assert  absolutely  that 
S  wherever  found  indicates  ^'s  present  existence,  is  to 
assert  that  every  S  without  exception  possesses  the 
attribute,  belongs  to  the  class,  deserves  the  name,  or  is 
found  in  conjunction  with,  ^ :  to  assert  the  same  re- 
servedly is  to  assert  that  S  and  ^  are  more  or  less  often 
found  together  (or  that  S  is  nearly  always,  usually, 
frequently,  ^) — more  often  than  mere  coincidence  will 
account  for,  -or  again  that  the  observed  conjunction  S 
and  ^  in  co-existence  will  at  least  tend  to  recur.  To 
assert  absolutely  that  S  wherever  found  indicates  ^'s 
future  existence  is  to  assert  not  only  that  S  is  a  cause 
(or  the  cause)  of  §b>  t>ut  that  no  other  cause  is  ever 
capable  of  interfering  with  it, — a  very  large  assertion :  to 
assert  the  same  reservedly  is  to  assert  that  S,  unless 
something  unspecified  interferes,  may  serve  as  a  sign  that 

*  To  say  that  S  icas  the  sole  cause  generally  bears  a  quite  different 
meaning,  namely  that  some  other  thing  (perhaps  vaguely  specified)  wag 
not  operative. 

t  See  note  at  p.  81. 
13 


270  FALLACIEa  [Part  II. 

^  will  happen,  or  tliat  the  observed  sequence  S  followed 
by  ^  will  tend  to  recur.  ^^ 

In  spite  of  these  tangled  variations  there  is,  as  it 
seems  to  me,  a  sufficient  reason  for  framing  the  formula 
as  above.  This  is  the  ideal  type,  by  comparison  with 
which  any  actual  shortcomings  may  best  be  made 
apparent.  If  S  does  not  indicate  §b  quite  absolutely, 
there  is  no  better  means  of  seeing  why  and  how  far  it 
falls  short  of  doing  so,  than  an  inquiry  what  are  the 
dangers  to  which  such  certainty  is  exposed  and  what 
has  been  done  to  guard  against  them.  And  as  for  the 
time-element,  that  may  be  neglected,  so  far  as  a  first  out- 
lined view  of  the  dangers  is  concerned.  Just  as  the 
process  may  be  generalised,  so  may  the  dangers.  In 
spite  of  their  surface  variations  their  deepest  meaning  is 
the  same.  There  is  at  bottom  one  primary  source  of 
fallacy  in  the  inductive  argument,  call  it  by  whatever 
name  may  be  most  convenient.  We  may  name  it,  for 
instance,  the  danger  of  "  overlooking  Plurality  of  Causes, 
or  neglecting  possible  Chance  or  Counteraction,"  or  "  the 
possibility  of  unknown  antecedents,"  or  "  arguing  either 
post  hoc  ergo  propter  hoc  or  per  enwmerationem  simpli- 
cem"  or  " neglecting  to  exclude  alternative  possibilities," 
or  "  forgetting  that  facts  may  bear  more  than  one  inter- 
pretation," or  "  stating  the  law  too  widely,"  or  "  failing 
to  see  below  the  surface,"  or — perhaps  on  the  whole  best 
of  all — "  unduly  neglecting  points  of  difference." 

It  may  be  well  here  to  make  a  slight  digression  in 
order  to  show  more  definitely  how  '  undue  neglect  of  dif- 


Chap.  "VL]       THE  EMPLOYMENT  OF  GUESSWORK.  271 

ference '  is  the  main  danger  of  direct  generalisation  just 
as  of  the  argument  from  analogy.  Concrete  evidence  for 
an  abstract  law  consists,  it  has  been  said,  of  a  case  or  cases 
brought  forward,  of  which  such  law  is  asserted  to  be  the 
best  explanation.  If  then  some  better  explanation  is 
possible  the  theory  as  stated  is  impeachable.  But  what 
is  meant  by  a  better  explanation  ?  Can  there  be  degrees 
of  explanation,  so  long  as  the  facts  are  all  explained  ? 
Surely  the  facts  relied  upon  either  do  or  do  not  all  form 
cases  under  the  law  asserted  ?  Surely  the  term  '  better ' 
or  '  worse '  is  inappropriate  ?  By  the  best  explanation  is 
meant,  however,  not  only  any  law  from  which  all  the 
facts  observed  are  deducible, — for  we  may  often  frame 
many  different  hypotheses,  inconsistent  with  each  other, 
which  will  each  explain  all  the  facts ;  but  what  is  meant 
is,  that  solitary  one  out  of  all  possible  hypotheses  which, 
while  explaining  all  the  facts  already  in  view,  is 
narrowed,  limited,  hedged,  or  qualified,  sufficiently  to 
guard  in  the  best  possible  way  against  undiscovered  ex- 
ceptions also.  The  wider  the  law  the  greater  the  danger, 
until  precautions  are  taken :  and  it  is  in  the  strength  of 
these  precautions  that  the  value  of  any  Theory  lies.  It 
is  a  merely  negative  condition,  or  absolute  sine  qud  non, 
that  a  Theory  shall  at  least  explain  the  facts  already  in 
view:  failing  this,  it  is  condemned,  or  seen  to  need 
qualification,  on  the  threshold.  But  beyond  and  above 
the  preliminary  condition  that  no  known  fact  as  yet  con- 
tradicts the  theory,  we  need  also  the  assurance,  in  some 
shape  or  other,  that  if  there  were  exceptions  (or  con- 


272  FALLACIES.  [Pabt  If. 

tradictory  instances)  their  existence  would  already  have 
been  discovered  or  inferrible.  This  assurance  it  is  which 
forms  the  turning-point  of  inductive  proof.  Hence  the 
'best'  explanation  of  the  facts  A  and  B  and  C  is  that 
explanation  which  while  neglecting  certain  points  of 
difference  among  them,  and  thus  forming  some  generalisa- 
tion, neglects  only  those  differences  which  are  'un- 
essential:' the  best  explanation  of  {i.e.  generalisation 
from)  one  solitary  sequence  observed  is  that  which 
neglects  only  its  unessential  elements  or  features.  While 
all  generalisation  exists  by  neglecting  points  of  difference, 
the  soundness  of  any  generalisation  consists  entirely  in 
the  completeness  with  which  it  balances  out  the  relative 
importance  of  the  points  of  difference  concerned.  The 
assumption  at  the  bottom  of  all  our  explanation  and  pre- 
diction— of  all  our  reduction  of  Nature  to  Law — is  not 
only  that  the  same  antecedents  will  have  the  same  con- 
sequents (for  it  seems  hardly  necessary  to  say  that  no 
two  total  sets  of  circumstances  ever  were  or  will  be 
precisely  alike  *),  but  that  whenever  some  of  the  observed 
circumstances  recur,  some  of  the  same  antecedents,  con- 
comitants and  consequents  may  be  looked  for.  The 
problem  is  always  to  discover  exactly  which  of  the  com- 
ponent circumstances  of  one  total  event  are  essential  to 
any  given  portion  selected  from  those  of  another.  Every 
abstract  proposition  selects  some  only  as  being  essential, 

•  Just  as  the  members  of  every  class  of  objects  have  their  points  of 
dissimilarity  from  each  other,  as  well  as  the  points  of  similarity  which 
constitute  them  a  class,  so  have  the  members  of  any  class  of  events. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORk.  273 

and  it  is  through  deep  analysis  of  the  actual  circumstances 
that  we  avoid  selecting  too  few.  The  two  opposite 
modes  of  missing  the  ideal,  then,  are : — (1)  to  be  content 
with  too  little  repetition  of  circumstances — too  broad  a 
law, — as  when  we  say  in  our  haste  "  All  men  are  liars," 
and  (2)  to  demand  too  exact  a  repetition  of  circumstances 
— too  narrow  a  law, — as  in  the  case  of  the  Chinaman  who 
burnt  doMm  his  house  in  order  to  repeat  as  far  as  possible 
the  exact  circumstances  in  which  he  first  obtained  a 
certain  kind  of  cookery.  The  former  fault  is  the  induc- 
tive fallacy  proper :  the  latter  may  be  a  serious  hindrance 
to  knowledge,  or  may  lead  to  a  waste  of  time  or  money 
or  trouble,  but  it  makes  no  false  pretence  and  thus  runs 
less  risk  of  failure  in  obtaining  the  immediate  efiect 
required. 

It  is  in  every  case,  then,  through  undue  neglect  of  the 
essential  difference  between  the  specific  case  or  cases 
observed  and  the  wider  genus  to  which  the  assertion 
professes  to  refer,  that  we  rise  to  a  generalisation  not 
sufficiently  guarded  against  possible  exceptions.  The 
ideal  is,  to  frame  every  generalisation  unexceptionably, — 
so  that  no  exception  can  be  found, — and  this  whether 
the  outward  form  that  the  statement  takes  is  simple — as 
in  "All  matter  gravitates," — or  qualified,  as  in  "All 
stones  fall  to  the  ground  except  when  restrained  in 
certain  ways  from  doing  so."  It  is  either  by  far-reach- 
ing foresight  or  by  growing  experience  that  exceptions 
come  to  light;  and  when  they  are  recognised,  the 
supposed  law  has  either  to  be  abandoned  altogether  (if 


274  '  FALLACIES.  [Paet  IL 

ihey  are  numerous  and  important)  or  modified  in  order 
to  take  them  in.  The  experimental  methods  are  thus, 
in  one  aspect,  methods  for  as  far  as  possible  anticipating 
the  discovery  of  exceptions. 

The  first  and  weakest  remedy  against  stating  as  a  law 
at  all,  what  should  properly  be  called  a  coincidence,  is 
the  employment  of  the  Theory  of  Probabilities:  an 
immense  subject,  and  fuU  of  dangers  of  its  own.  Any 
full  discussion  of  its  details  is  here  out  of  the  question  ;  * 
nor,  indeed,  is  it  required  for  our  purposes.  It  may,  how- 
ever, be  explained  that,  as  regards  Proof  and  Disproof — 
i.e.  as  regards  the  simple  answer  Yes  or  No,  to  a  question 
raised  and  debated, — the  chief  operation  of  the  doctrine 
is  in  enabling  us  to  say  in  certain  cases  that  S  and  ^ 
(e.g.  sun-spots  and  magnetic  storms)  occur  in  conjunc- 
tion more  frequently  than  can  be  accounted  for  by  mere 
coincidence.  In  the  absence  of  any  knowledge  of  the 
causation  concerned,  such  a  result  may,  no  doubt,  have  a 
certain  value.  But  in  pursuance  of  our  plan,  we  shaU 
confine  attention  to  the  more  marked  and  definite  end 
of  the  scale.  The  employment  of  the  Doctrine  of  Chances 
must  always  be  superseded  by  more  stringent  methods  as 
soon  as  inquiry  passes  beyond  its  very  earliest  and  most 
tentative  stages. 

Since,  then,  for  complete  proof  of  a  law  from  facts 
two  things  are  necessary : — 

•  Mr.  Venn's  Logic  of  Chance  is  generally  considered  the  best 
English  work  on  the  subject.  See  also  Mill's  Logic,  bk.  iii.  chaps,  xrii. 
XFiii.  and  xxiii.  j  and  Bain's  Induction,  chap.  ix. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  275 

(1)  The  assurance  that  no  contradictory  instance  has 

yet  been  found,  and 

(2)  The  assurance  that  if  a  contradictory  instance 

existed  its  existence  would  be  known : 
it  follows  that  negatively  all  turns  on  the  finding  of  con- 
tradictory instances,  while  'positively  all  turns  on  the 
completeness  of  the  search  for  them.  All  positive  proof 
depends  not  on  the  fact  of  observations  having  been  made 
nor  even  on  the  fact  of  experiments  having  been  per- 
formed; but  on  the  care,  the  precautions,  with  which 
observation  has  been  interpreted  and  experiment  con- 
ducted. So  far  only  as  these  exclude  alternative 
possibilities,  are  they  of  real  value. 

We  have  noticed,  more  than  once,  the  danger  of  over- 
looking alternative  possibilities.  And  it  is  true  that 
every  Theory  set  up  has,  in  the  first  place,  to  show  its 
preferability  over  all  conflicting  theories.  This  is  pre- 
cisely what  is  meant  by  saying  that  the  burden  of  proof 
remains.  Just  because  Disproof  is  easier  than  Proof,* 
and  because  all  positive  assertion  can  only  justify  itself 
as  a  remainder  when  negative  assertions  are  subtracted — 
when  mistakes  have  been  either  one  by  one  eliminated 
or  in  a  body  prevented — the  burden  of  doubt  to  be 
removed  by  evidence  consists  essentially  in  the  group  of 
alternative  theories  remaining  undiscarded.  The  impor- 
tant point  is  always,  to  show  that  all  other  possible 
theories  are  weighed  in  the  balance  and  found  wanting : 
that  is  to  say,  that  all  precautions  have  been  taken  against 
•  See  p.  250. 


276  FALLACIES.  [Paet  n. 

that  crudest  kind  of  unchecked  generalisation  which  the 
least  trained  mind  possesses  ever  in  greatest  abundance. 

This  objection  against  a  theory — that  alternative 
theories  are  not  yet  discarded — appears,  however,  more 
directly  applicable,  more  fruitful  of  results,  against  a 
concrete  or  an  abstract-concrete  thesis  than  against  a 
directly  abstract  one  ;  and  as  a  method  of  attack  on  such 
theses,  where  for  any  reason  it  may  be  inconvenient  to 
search  for  the  supposed  underlying  Principles,  it  could 
no  doubt  be  made  useful.  Accordingly  I  have  thought 
it  worth  while  to  set  out  in  an  Appendix  (A)  a  sum- 
mary of  the  alternative  theories  amongst  which  any 
observed  concrete  sequence  or  coexistence  has  to  choose. 
Every  observation  or  experiment  interpreted  is  a  case  of 
the  assertion  of  an  abstract-concrete  proposition.  Find- 
ing S  followed  or  accompanied  by  ^,  under  certain  con- 
ditions, we  assert  causal  connection  between  them.  And 
the  right  of  the  theory  chosen,  over  all  its  possible  rivals, 
depends  entirely  upon  the  depth  of  our  insight  into  the 
conditions  under  which  the  experiment  or  observation 
was  really  made.  This  is  the  main  lesson  of  Logic,  as 
regards  Induction.  The  illogical  person  is  content  to 
produce,  as  evidence  for  a  supposed  instance  of  causation, 
the  bare  fact  of  succession  in  time,  or  unexplained  con- 
comitance,— as,  for  example,  in  the  case  of  quack  re- 
medies, or  again,  in  nearly  all  cases  of  superstitious 
belief;  while  inductive  science  always  demands  as 
full  an  analysis  as  possible,  of  all  the  circumstances. 
Failing  this,  as  with  all  care  it  must  sometimes  fail,  the 
proof  is  recognised  as  weak. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  277 

(c)  The  Empirical  Methods. 

Of  Empirical  Methods  the  only  careful  classification 
yet  made  is,  I  believe,  Mill's  well-known  list  of  five. 
While,  as  their  author  himself  (and  more  lately.  Professor 
Jevons)  expended  labour  in  showing,  none  of  these  is, 
except  in  an  ideal  sense,  completely  satisfactory  as  a 
guarantee,  but  in  every  case  a  further  assertion  is 
practically  wanted;  yet  the  statement  of  the  method 
employed  in  the  given  experiment  or  observation,  to- 
gether with  the  precautions  taken  against  its  special 
dangers,  may  be  regarded  as  the  answer  given  to  the 
challenge  of  possible  alternatives :  in  other  words,  as  a 
means  of  shifting  the  burden  of  proof. 

Since  there  may  possibly  be,  in  some  quarters,  a  dis- 
position to  take  these  methods  for  more  than  they  were 
probably  intended  to  be  worth,  there  will  perhaps  be  some 
use  in  reminding  the  reader  that  it  is  the  guarding 
against  the  danger  to  which  each  method  is  liable,  that 
is  in  every  case  the  all-important  circumstance — far  more 
so  than  the  mere  employment  of  this  or  the  other 
method.  It  is  not,  for  instance,  because  a  given  experi- 
ment "  proceeds  according  to  the  Method  of  Difference  " 
that  the  evidence  is  strong,  but  because  by  means  of 
certain  precautions  (often  more  easily  taken  under  the 
Method  of  Difference  than  in  the  other  cases)  we  happen 
to  have  approximately  reached  the  ideal  there  set  up. 
A  careful  employment  of  the  "  weakest "  of  the  methods 
is  often  better  than  a  loose  employment  of  the  strongest. 


278  FALLACIEa  [Paet  II. 

It  seems  unnecessary  in  this  place  to  obscure  our 
more  general  view  by  entering  upon  the  Empirical 
Methods  in  detail  and  discussing  their  special  liabilities 
to  frustration.*  It  will  be  enough  here  to  remark  that 
ultimately  the  sole  danger  of  fallacy  in  empirical  proof 
is  that  of  neglecting  to  take  into  account  the  differences 
between  the  Antecedent  (or  Consequent)  observed  in 
any  actual  sequence,!  and  that  spoken  of  in  the  S  (or  ^) 
of  our  abstract  proposition  based  upon  it.  In  any 
sequence  observed  in  Nature  there  are  usually  certain 
elements  overlooked  at  first,  and  if  one  of  these  be 
important,  our  'natural'  inference  is  to  that  extent 
misguided.  Thus  for  a  long  time  the  possibility  was 
overlooked  that  the  phenomena  of  fermentation  could  be 
due  to  germs  floating  in  the  air.  From  the  most  careful 
experiments  that  were  made  up  to  the  beginning  of  the 
present  century,  the  belief  was  held  that  since  all  the 
possible  external  sources  were  known  and  guarded 
against,  the  generation  of  the  yeast-plant  must  take 
place  in  some  'spontaneous'  fashion  within  the  fluid 
itself  So  again,  until  quite  recently  it  was  commonly 
believed  that  the  carbon  of  vegetable  produce  must  come 
from  the  soil :  that  it  should  be  almost  entirely  derived 
from  colourless  air,  seemed  on  the  face  of  it  unlikely. 

The  same  danger  may  be  otherwise  phrased  by  saj'^- 

•  I  have,  however,  thought  it  well  to  set  these  out  in  the  Appendix 
(B). 

f  For  brevity  I  here  speak  of  sequence  only ;  since  unless  causation 
be  a  dream,  co-existence  may  always  be  reduced  to  a  complex  result  of 
sequences.     See  also  Appendix  (A). 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  279 

ing  that  the  empirical  fallacy  consists  ia  resting  our 
proof  of  a  law  or  theory  on  confirmatory  (i.e.  congruent) 
facts  alone.  If  the  facts  around  us  do  not  fit  our  theories 
we  have  of  course  unanswerable  disproof:  but  if  the 
facts  do  fit  them,  the  theories  are  not  yet  necessarily 
secure.  We  need  besides  such  facts,  in  every  case  the 
further  assurance  that  any  contradictory  facts,  if  existing,' 
would  have  come  to  light.  And  so  far  as  this  assurance 
is  wanting,  so  far  the  proof  is  weak.  Mere  number  of 
confirmatory  facts  will  sometimes  yield  us  this  assurance, 
but  only  so  far  as  in  the  given  case  the  special  circum- 
stances guarantee  this,  is  number  of  any  avail.  In  many 
cases  (e.g.  in  most  chemical  experiments)  a  single  instance 
is  more  trustworthy  than  a  thousand  of  another  kind, 
since  here  the  precautions  are  often  enough  to  exclude 
'  unknown  antecedents.'  The  assurance  lies  outside  any 
inductive  methods :  for  the  various  methods  merely  cor- 
respond to  various  forms  which  the  same  difficulty  takes 
on.  It  is  analysis  only  that  can  enable  us  to  know  how 
far  we  have  really  reckoned  with  unknown  antecedents, 
— analysis  of  the  complex  facts  presented  to  our  obser- 
vation. The  whole  difference  between  sound  and  un- 
sound generalisation  lies  in  the  care  with  which  we  seek 
for  hidden  elements  in  the  cases  observed,  which  shall 
modify  our  first  rough  guess  at  the  law  supposed  to 
explain  them. 

Accordingly  the  attack  on  a  generalisation  most 
usefully  takes  the  shape  of  an  attempt  either  directly  to 
point  out  hidden  circumstances  in  the  facts  observed. 


280  FALLACIES.  [Pabt  H. 

or  at  the  least  to  point  out  that  the  analysis  has  not 
been  a  remarkably  searching  one.  Thus  Pro£  Tyndall, 
attacking  the  theory  that  Bacteria  are  capable  of  '  spon- 
taneous generation,'  sums  up  the  chief  faults  of  the 
argument  as  follows  : — 

"  The  proof  of  Bacterial  death  at  140°  Fahr.  consists  solely  in  the 
observed  fact,  that  when  a  certain  liquid  is  heated  to  that  temperature 
no  life  appears  in  it  afterwards ;  while  in  another  liquid  life  appears 
two  days  after  it  has  been  heated  to  212°.  Instead  of  concluding  that 
in  the  one  liquid  life  is  destroyed  and  in  the  other  not,  it  is  assumed 
that  140°  Fahr.  is  the  death-temperature  for  both  ;  and  this  being  so, 
the  life  observed  in  the  second  liquid  is  regarded  as  a  case  of  spon- 
taneous generation.  A  great  deal  of  Dr.  Bastian's  most  cogent  reason- 
ing rests  upon  this  foundation.  Assumptions  of  this  kind  guide  him 
in  his  most  serious  experiments.  He  finds,  for  example,  that  a 
mineral  solution  does  not  develop  Bacteria  when  exposed  to  the  air  ; 
and  he  concludes  from  this  that  an  organic  infusion  also  may  be  thus 
exposed  without  danger  of  infection.  He  exposes  turnip-juice  accord- 
mgly,  obtains  a  crop  of  Bacteria,  which,  in  the  light  of  his  assumption, 
are  spontaneously  generated.  Such  are  the  warp  and  woof  of  some  of 
the  weightiest  arguments  on  this  question  which  have  been  addressed 
by  him  to  the  Royal  Society." 

Finding  M  (a  component  of  Sj  followed  or  accompanied 
by  Z,  whether  in  numerous  instances,  or  in  one  instance 
where  apparently  no  third  circumstance  has  had  time 
or  opportunity  to  intervene,  the  natural  impulse  is  to 
state  the  law  as  M  — >  Z.  And,  in  every  case,  attack 
on  the  trutli  of  such  law  consists  ultimately  either  in 
the  direct  assertion  that  certain  instances  do  in  fact 
contradict  it,  or  in  the  milder  assertion  that  no  steps 
have  been  taken  to  limit  the  sweep  of  the  law  as  far  as 
prudence  would  suggest;  or  in  the  still  milder  shape 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  281 

of  an  inquiry  whether  or  no  such  steps  have  been  taken. 
If,  in  the  case  observed,  M  or  Z  was  really  qualified  by 
the  presence  of  N,  it  is  always  possible  that  the  real 
law  may  be  N  — >  Z,  or  MN  — >  Z,  or  M  — >  ZN,  or 
MN  — >  ZN ;  that  is,  N  may  be  an  important  factor, 
and  any  statement  of  the  law  which  neglects  to  mention 
it  may  accordingly  be  inexact  and  misleading. 

In  the  Appendix  it  is  noticed  that  the  five  methods 
consist  really  of  variations  upon  two  that  are  funda- 
mental. These  two  are  the  Methods  of  Agreement 
and  of  Difierence.  It  is  questionable,  however,  whether 
the  distinction  even  between  these  two  is  of  real  import- 
ance from  our  point  of  view.  As  regards  observed 
coexistences,  the  Method  of  Difference  is  plainly  alto- 
gether inapplicable  until  they  are  resolved  into  sequences 
(which  is  often  at  present  practically  impossible) ;  but 
as  regards  sequences  the  distinction  depends  merely  on 
the  fact  that  in  employing  the  Method  of  Agreement 
•  unknown  circumstances '  are  eliminated  chiefly  by  the 
number  and  variety  of  observations,  while  in  employ- 
ing the  Method  of  Difference  it  is  chiefly  the  immediacy 
of  the  sequence  (known  through  our  control  of  surround- 
ing conditions)  that  is  relied  upon  for  the  same  pur- 
pose. But  in  both  we  may  be  deluded,  and  by  the 
same  cause.  The  case  or  cases  upon  which  we  rest  our 
theory  may  really  belong  to  a  narrower  class  than  that 
which  the  theory  contemplates.  Their  differentia  over 
the  genus  about  which  we  make  the  assertion,  may  be  an 
important  factor  in  the  behaviour  of  the  things  observed. 


282  FALLACIES.  [Part  1L 

The  Five  Inductive  Methods,  with  all  their  unlike- 
ness  to  each  other,  have  thus  one  important  point  of 
similarity.  They  all  consist  in  bringing  cases, — claimed 
to  be  unmistakable  on  account  either  of  their  '  nature ' 
and  circumstances,  or  their  number  and  variety, — cases 
of  the  operation  of  the  law  set  up  as  Thesis,  and  of  no 
more  complex  one.  And  consequently  the  one  point  of 
vulnerability  for  all  of  them  is  the  possibility  that  the 
cases  relied  upon  were  somehow  different  from  thoso 
expressly  covered  by  the  law ;  that,  in  fact,  there  were 
special  circumstances  along  with  them,  which  should  be 
generalised  so  as  to  find  expression  in  the  statement  of 
the  law,  making  it  narrower  than  at  present. 

The  five  methods  are  not  in  themselves  a  set  of 
separate  safeguards  against  inductive  fallacy,  or  a  com- 
plete exposition  of  the  modes  in  which  we  oughi  to 
reason  from  fact  to  law  ;  but  rather  a  generalised  analysis 
of  some  of  the  most  elementary  modes  in  which  we  do 
(or  perhaps,  did  originally)  so  reason;  each  of  these 
modes  being  liable  to  its  own  special  dangers,  and  there- 
fore, unless  properly  guarded,  each  and  all  being  illusory 
as  a  guarantee.  Regarded  simply  as  methods  of  Proof, 
they  are  in  several  ways  not  quite  satisfactory.  They 
are  in  this  dilemma :  either  they  are  to  be  used  as  actual 
tests,  to  which  we  can  bring  the  given  experiment, — in 
which  case  they  are  certainly  liable  to  '  frustration ; '  or 
else  they  are  merely  ideals  to  which  in  practice  we  can 
never  be  sure  that  we  attain.  Moreover,  they  assume  a 
greater  simplicity  of  material  than  really  ever  exists,  and 


Chap.  "VL]       THE  EMPLOYMENT  OF  GUESSWOHK.  283 

they  assume  too  that  the  mind  comes  to  its  work  of 
interpreting  the  facts  of  experience  in  a  state  of  candour 
and  virgin  ignorance  which  is — ever  since  language  took 
shape — ver}'^  far  from  being  the  actual  case.  Their 
practical  value,  therefore,  is  rather  as  systematic  hints 
for  tentative  discovery,  than  as  methods  of  Proof  at  alL 

How  then  is  our  general  knowledge  proved  from  the 
particular  facts  of  experience  ?  It  can  be  disproved  by 
experience  easily  (subject  of  course  to  the  familiar 
possibility  of  our  supposed  experience  being  itself  illusory), 
but  proof  of  an  abstract  proposition  can  never  be  theoreti- 
cally complete,  and  the  lines  which  we  draw  across  the 
long  scale  between  the  highest  practical  certainty  and 
the  wildest  guess-work  are,  like  all  our  distinctions  in 
continuous  nature,  useful  up  to  a  certain  point  but 
incapable  of  standing  close  scrutiny  or  careful  refine- 
ment. The  truth  that  destruction  is  easy  and  construc- 
tion difficult,  is  nowhere  better  exemplified  than  in  our 
proof  of  general  laws.  A  sequence  in  Nature  is  observed 
to  happen  frequently ;  this  perhaps  sets  some  ingenious 
inquirer  on  the  track  of  a  law ;  experiments  (we  are 
speaking,  of  course,  of  modern  times),  are  made  with  the 
view  of  testing  the  hypothesis, — of  narrowing  down  the 
law  into  definiteness  and  limiting  it  as  far  as  necessary. 
At  last,  after  many  struggles  it  comes  forth  as  a  recog- 
nised empirical  law.  But  now  it  either  remains  in  this 
condition,  with  the  sword  of  possible  contradictory 
instances  ever  hanging  over  its  head,  or  by  some  further 
discovery  it  gets  established  under  the  protection  of 


284  FALLACIES.  [Part  II. 

some  wider  law  with  a  greater  prescriptive  right.  Now, 
if  it  be  false,  this  wider  law  must  be  false  also.  Perhaps 
it  is  secure  at  last  ?  Perhaps  it  may  be ;  practically  it 
often  is,  but  theoretically  never.  For  every  supposed 
law  has  merely  served  its  purpose  and  stood  its  tests 
(such  tests  as  we  can  apply)  for  a  certain  finite  length 
of  time.  After  centuries  of  life  it  may  be  upset  in  a 
moment,  or  at  least  found  to  be  not  universally  true,  to 
be  true  only  under  conditions,  to  be  crude  in  its  present 
statement  and  to  need  further  refining  away.  The 
longer  it  has  stood  its  trial,  the  safer  of  course  it  is 
against  the  fear  of  contradictory  instances  coming  to 
light ;  in  fact,  it  has  probably  been  pared  down  already 
to  accommodate  such  instances  a  dozen  times,  being  of 
course  narrowed  each  time. 

It  is  an  ungrateful  task  for  any  one  who  cares  about 
the  distinction  between  truth  and  error,  to  dwell  on  such 
facts  as  these,  without  some  further  apology.  They 
seem  at  first  sight  to  prove  too  much, — namely  that 
there  is  no  certainty  ever  attainable  in  interpreting 
Nature,  but  that  '  unknown  antecedents '  are  as 
ubiquitous,  and  possibly  as  destructive  to  our  best  theories, 
as  the  dangers  to  health  in  the  midst  of  which  our  lives 
are  passed.  Nor  do  I,  in  fact,  see  any  way  of  denying 
this  except  by  means  of  deliberate  self-deception.  But 
such  apology  as  I  can  make  for  this  view  will  come 
better  in  speaking,  at  the  end,  of  some  of  the  defences 
that  can  be  made  for  Logic  as  a  practical  science. 

Of  course,  in  the  case  of  a  great  many  laws  believed 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  285 

in,  the  question  is  settled  for  us  by  ancestral  habits ;  and 
in  many  other  cases  we  shall  accomplish  more  in  the 
world  by  faith  than  by  scepticism.  But  here  we  are 
merely  trying,  for  the  moment,  to  see  the  facts  as  they 
are,  and  not  as  practical  prudence  might  suggest  that  we 
had  better  habitually  view  them.  And  two  things,  I 
think,  we  cannot  help  admitting : — 

First,  that  every  supposed  law,  whether  of  succession 
or  coexistence,  may  turn  out  to  be  too  widely  stated- 
If,  as  is  probable,  there  is  '  some  truth  in '  such  law,  yet 
the  assertion  it  makes  may  be  too  wide  and  sweeping, 
and  perhaps  ought  to  be  limited  in  some  way,  making 
it  true  only  under  certain  conditions. 

Secondly,  between  mere  guesses,  hypotheses,  theories, 
empirical  laws,  and  'laws  of  Nature,'  there  are  only 
continuous  differences  of  degree  in  certainty,  according 
to  the  nature  and  number  of  the  tests  they  have  stood, 
and  the  duration  of  their  past  invulnerability.  In  the 
case  of  Axioms,  so  far  as  their  contradictory  is  incon- 
ceivable— i.e.  makes  nonsense  of  the  words  employed, — 
so  far  of  course  it  is  futile  to  speak  of  their  uncertainty ; 
but  wherever  this  is  not  the  case.  Axioms  too  come 
merely  at  the  head  of  this  same  scale  of  credibility.  The 
resemblance  in  uncertainty  between  a  fanciful  guess  and 
a  proved  law  may  be  less  important  than  the  difference 
in  degree  of  certainty:  but  the  fact  cannot  be  safely 
hidden  that  the  resemblance  exists. 

The  distinction  often  made  between  valid  inductions 
and  'merely  empirical  laws'  is  then,  strictly  speaking, 


286  TALLACIES.  [Pabt  IL 

not  absolute,  though  roughly  useful;  the  line  between 
them  will  not  bear  close  inspection.  For  *  empirical ' 
means  '  true  so  far  as  we  can  yet  see,  but,  inasmuch  as 
inexplicable  at  present  by  a  higher  law,  possibly  liable  to 
further  limitation ; '  and  this  may  be  said  of  every  Law 
of  Nature  we  possess.  The  method  of  proving  laws  is 
one  and  the  same  whether  they  be  the  merest  wildest 
supposition  or  the  soundest  explanation  of  the  facts  of 
Nature.  In  the  first  place  it  is  a  sine  qua  non  that  no 
contradictory  instance  shall  have  yet  been  found.  It 
hardly  needs  expressly  stating  that  one  single  discovered 
exception  is  sufficient  to  break  down  an  asserted  law. 
The  absence  of  such  an  instance,  however,  it  must  be 
equally  obvious,  is  not  sufficient  for  proof.  But,  in  the 
second  place,  the  positive  strength  of  our  evidence  de- 
pends upon  the  extent  of  our  right  to  claim  sufficient 
knowledjje  of  all  the  attendant  circumstances  of  the 
observation  or  experiment. 

IV.  The  Dangers  of  the  Argument  by  Sign. 

Tinder  Deductive  Proof,  it  will  be  remembered,  we 
have  elected  to  leave  aside  the  case  of  complete  Demon- 
stration, since  to  supply  a  missing  premiss  correctly  is 
at  least  as  difficult  as  to  pass  it  for  sufficient  when 
already  expressed.  It  is  not,  however,  with  the  whole 
problem  of  supplying  missing  premisses  that  we  are 
now  concerned :  that  belongs  by  right  to  the  method  for 
reducing  to  absurdity. 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  287 

What  is  here  called  the  argument  by  sign,  as  opposed 
to  the  argument  by  example,  consists  of  the  cases  where 
the  major  premiss  is  either  itself  given  as  Reason,  or  is 
only  suppressed  through  its  extreme  familiarity,  not 
through  any  doubt  as  to  its  truth  or  any  hesitation  as  to 
what  the  law  may  really  be.  When,  e.g.,  we  attempt  to 
prove  innocence  by  means  of  an  alihi,  we  refer  no  doubt 
to  the  principle  (which  hardly  needs  express  statement) 
that  a  man  cannot  be  in  two  places  at  once ;  and  so,  in  a 
large  number  of  instances,  where  the  application  alone  is 
expressly  given,  the  argument  is  really  intended  for  deduc- 
tive. In  all  cases  of  attempted  proof,  it  is  experience  in 
some  shape  or  other  that  is  relied  upon,  whether  already 
generalised  experience  or  not ;  experience  crystallised 
into  names  and  propositions,  or  experience  not  yet  so 
formulated.  The  difference  between  empirical  and  de- 
ductive proof  may  be  further  brought  out  by  saying  that 
in  the  former  we  deal  more  directly  with  the  facts  expe- 
rienced, while  in  the  latter  we  rely  largely  on  mere  for- 
mulas. 

The  chief  difficulties  in  summing  up  the  dangers 
peculiar  to  the  Argument  by  Sign  lie  partly  in  the  fact 
that  faulty  deduction  may  be  due  to  so  many  different 
causes,  and  that,  through  disclaiming  one  cause  while 
allowing  another  to  operate,  the  fallacy  has  so  many 
facilities  for  escaping  open  conviction ;  and  partly  in  the 
fact  that  according  to  our  own  definition,  it  is  only  when 
both  Principle  and  Application  are  clearly  apprehended 
as  such,  that  any  argument  can  be  rightly  called  deduc- 


288  FALLACIES.  [Part  IL 

tive,  and  that  consequently  if  an  attempt  is  made  to 
employ  a  Principle  that  does  not  strictly  apply,  it  may 
easily  be  pleaded  against  the  charge  of  faulty  deduction, 
that  strict  deduction  (Demonstration)  is  not  intended. 

Nevertheless  something  may,  I  think,  be  done,  by 
recognising  clearly  that  the  danger  against  which  every 
argument  professedly  deductive  has  to  guard  is  the  ac- 
ceptance of  a  Principle  which  does  not  apply ;  and  this, 
whether  caused  through  ignorance  of  syllogistic  require- 
ments, or  through  verbal  ambiguities,  or  through  suppos- 
ing the  reciprocal  of  either  Principle  or  Application  to  be 
its  equivalent.  Against  the  easy  plea  that  demonstration 
is  not  intended,  may  be  brought  the  reminder  that  in  such 
case  the  Thesis,  so  far  as  definitely  asserted,  is  at  first  a 
pretender  to  qualities  which  it  afterwards  confesses  to 
be  wanting.  So  far  as  it  really  cannot  be  rationalised, — 
by  bringing  the  underlying  principle  and  its  application 
into  shape  for  rigid  investigation, — so  far  its  truth  must 
of  course  remain  untested,  and  belief  in  its  truth  either 
a  careless  or  a  semi- voluntary  act. 

It  may  be  well,  then,  to  glance  at  the  operation  of 
the  three  causes  of  faulty  deduction  just  above  enume- 
rated. And  first,  of  the  ignorance  of  syllogistic  require- 
ments. By  this  is  meant  solely  the  ignorance,  when 
Reason  and  Thesis  are  given,  of  the  fact  that  a  further 
assertion  is  implied,  and  of  the  nature  and  limits  of  such 
further  assertion, — what  must  be  said  by  it,  in  order  to 
complete  the  deductive  proof. 

It  may  be  held,  and  it  may  be  true,  that  in  actual 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  289 

practice  purely  syllogistic  fallacies  very  rarely  occur. 
What  on  the  face  of  them  appear  like  syllogistic  fallacies 
may  in  most  cases  be  found  on  further  inquiry  to  be 
really  due  either  to  false  belief  as  to  the  matter,  or  to  the 
tyranny  of  names,  or  to  ignorance  of  the  law  of  Counter- 
Indication,  whereby  the  reciprocal  of  some  true  Principle 
is  accepted  as  equivalent  in  meaning.  Thus  if  any  one 
argues  that  the  prisoner  is  guilty,  from  the  fact  of  his 
confusion  when  arrested,  it  is,  no  doubt,  more  probable 
that  he  believes  in  the  truth  of  the  further  assertion 
'  confusion  — >  guilt,'  or  in  the  equivalence  of  this  with 
the  less  questionable  law  that '  guilt  causes  (and  there- 
fore — >)  confusion,'  than  in  the  formal  sufficiency  of  the 
latter  assertion  as  completing  the  Syllogism.  Still,  easy 
and  indeed  self-evident  as  the  formal  requirements  of 
reasoning  are,  we  are  bound  to  suppose  that  people  are 
occasionally  liable  to  look  upon  insufficient  premisses 
as  formally  binding.  In  fact,  there  is  probably  one  class 
of  persons  who  have  really  acquired  some  power  of  con- 
fusing themselves  in  this  matter,  namely,  those  who, 
having  learnt  the  moods  and  figures  by  rote  for  an 
examination,  have  not  as  yet  quite  succeeded  in  forget- 
ting them  again.  Nothing  could  well  be  more  confusing 
than  an  attempt  to  apply  the  cumbrous  machinery  of 
the  Syllogism  to  arguments  met  with  in  real  life.  And 
whoever  has  tampered  with  his  mother -wit  by  substi- 
tuting for  it  a  clumsy  Logic  depending  on  elaborate 
mnemonics,  must  no  doubt  pay  the  penalty  in  loss  of 
power,  so  long  as  the  mischief  remains. 


290  FALLACIES.  [Pabt  IL 

It  is  well,  therefore,  to  remember  that  the  Syllogistic 
requirements  may  always  be  clearly  shown  either  by 
viewing  the  middle  term  as  a  sign,  the  universal  trust- 
worthiness of  which  sign  is  all-important  to  the  proof; 
or,  where  the  middle  term  is  difficult  to  find,  by  viewing 
R  as  itself  the  affirmation  of  the  antecedent  (or  the  denial 
of  the  consequent)  of  a  hypothetical  proposition  of  which 
T  (or  the  denial  of  T)  forms  the  other  term.  It  is  not 
necessary  in  this  place,  however,  to  enter  fully  into  the 
details  of  this  operation,  since  in  the  chapter  on  Reduc- 
tion to  Absurdity  (p.  298)  we  shall  find  a  better  opportu- 
nity for  doing  so.  In  the  mean  time,  apart  from  igno- 
rance of  syllogistic  requirements,  and  from  the  possibility 
that  our  supposed  knowledge  relied  upon  may  be  mis- 
taken, there  remain  two  other,  and  commoner,  sources  of 
error. 

As  regards  the  acceptance  of  the  reciprocal  as  equiva- 
lent, not  much  more  remains  to  be  added  to  that  already 
said.  Either  the  Principle  or  the  Application  may  be 
wrongly  supplied  in  this  manner,  with  the  result  that 
we  then  accept  an  express  principle,  together  with  an 
express  supposed  application  thereof,  when  in  fact  the 
latter  is  merely  the  application  of  a  very  different  prin- 
ciple,— and  one,  it  may  be,  very  much  easier  to  prove. 
Especially  is  this  the  case,  as  pointed  out  above,  in  the 
disjunctive  (or  dilemmatic)  argument :  M  — >  non-^  is 
nearly  always  easier  to  establish  than  non-M  — >  ^ ; 
and  accordingly,  wherever  in  a  deductive  argument  the 
R  states  that  S  — >  non-M,  we  need  to  be  especially  on 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  291 

guard.  But  in  all  cases  of  attempted  deductive  proof, 
this  fallacy  is  a  constant  source  of  danger.  And  its  in- 
sidious nature  and  the  facilities  for  escape  which,  even 
when  detected  and  arrested,  it  presents,  mark  it  out  as 
deserving  very  careful  attention. 

So  great  are  the  facilities  for  escape  that  it  is  difficult 
to  find  instances  which  will  be  unhesitatingly  accepted  as 
such,  even  by  a  respectable  minority  of  readers.  The 
danger  is  so  simple,  so  obvious  when  pointed  out,  that 
those  who  liave  not  had  occasion  to  study  the  causes 
of  fallacy  in  actual  operation  will  be  loth  to  accuse  the 
human  intellect  in  general  of  ever  being  in  the  least 
affected  by  it :  while  even  those  who  have  watched  the 
action  of  erroneous  reasoning  most  carefully  must  hesitate 
to  say  in  the  given  case  that  this  cause  was  solely,  or  even 
mainly,  operative.  The  logician  is  in  fact  here  placed  in 
much  the  same  difficulty  as  so  frequently  occurs  in  all 
interpretation  of  motives:  several  motives  have  had  a 
share  in  some  action,  and  amongst  them,  in  the  vaguest 
and  most  unconscious  manner,  one  motive  less  noble  than 
the  rest ;  a  motive  which  the  person  accused  wiU  be  not 
only  sure  to  deny,  but  which,  if  he  had  been  conscious  of 
it  at  the  time  of  acting,  he  would  at  once  have  dismissed 
as  unworthy.  As  a  matter  of  fact  it  may  have  had  con- 
siderable weight,  and  yet  if  the  case  is  brought  forward 
as  an  instance  of  its  operation,  a  feeling  of  perfectly 
honest  virtuous  indignation  is  aroused.  So  it  is  with 
this  deductive  fallacy.  A  person  who  has  really  been 
partly  misled  by  it  will  be  almost  sure  to  declare,  when 


292  FALLACIEa  [Pabt  II. 

the  fallacy  is  pointed  out,  either  that  he  meant  the 
Principle  to  cut  both  ways,  or  else  that  he  only  intended 
to  make  a  suggestion  or  to  raise  a  presumption, — "  com- 
plete demonstration  being  unattainable : "  and  quite 
probably  both  of  these  intentions  were  really  present 
to  his  mind  in  a  vague  way,  along  with  some  uncertainty 
as  to  what  the  requirements  of  complete  demonstration 
might  be.  For  just  as  a  man  is  seldom  conscious  of  his 
own  motives  at  the  time,  while  on  after  reflection  the 
nobler  motives  are  apt  to  rise  into  undue  prominence, 
so  our  view  of  what  constitutes  complete  demonstraticm 
is  often  clearer  on  after  reflection  than  in  the  heat  of 
argument  or  during  the  first  glow  of  belief. 

Nevertheless,  there  is  on  occasion  something  gained 
by  forcing  even  the  most  unworthy  motives  into  promi- 
nence, in  order  that  they  may  be  definitely  disclaimed 
and  the  disclaimer  registered  for  future  use ;  and  so  with 
this  kind  of  fallacy.  Where  the  argument  is  plainly 
intended  for  deductive,  time  may  often  be  saved  by 
searching  first  for  any  slackness  in  the  view  of  what  de- 
ductive proof  really  demanda  If  on  inquiry  it  turns  out 
that  the  intention  was  merely  to  raise  a  loose  presumption 
in  favour  of  the  view,  the  looseness  of  the  presumption 
may  be  thus  made  fully  evident :  while  if  the  reciprocal 
of  the  express  principle  is  believed  to  be  also  true,  this 
belief  can  then  be  placed  on  its  trial. 

The  remaining  source  of  danger  in  deductive  argu- 
ments may  be  described  as  that  of  forgetting  part  of  the 
postulated  meaning  of  the  names  employed,  or  again,  of 


Chap.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  293 

reading  into  them  meanings  which  they  are  not  intended 
to  bear.  So  far  as  significant  names  are  employed  in 
Proof  (whether  as  M  or  S  or  ^)  the  two  liabilities  to 
error  are  at  bottom  the  same  as  those  already  men- 
tioned,— undue  neglect  of  difference  or  of  resemblance. 
The  meaning  of  every  name,  we  have  seen  (p.  108) 
contains  two  elements, — the  differential  and  the  generic, 
— and  either  of  these  may  be  unduly  overlooked.  We 
may,  in  other  words,  unduly  neglect  the  negative  or 
the  positive  meaning,  the  points  of  difference  from  other 
things  or  the  points  of  resemblance  to  some  of  them, 
to  which  the  name  refers. 

This  double  chance  of  error  is  one  that  was  treated 
at  some  length  by  Aristotle,  under  the  name  of  the 
Fallacia  Accidentis,  or  confusion  of  the  accidental  with 
the  essential  It  is  true  that  if  we  interpret  Fallacia 
Accidentis  as  widely  as  possible,  it  will  include  far  more 
than  these  merely  verbal  errors,  namely,  the  errors  also 
to  which  empirical  proof,  as  such,  is  liable.  When  we 
reason  by  false  Analogy,  or  when  we  explicitly  frame  too 
sweeping  a  generalisation,  we  are  taking  'accidental' 
resemblance  for  essential  (or  essential  difference  for  acci- 
dental) ;  and  vice  versd  when  we  fall  short  of  the  ideal 
on  the  other  side ;  but  it  was  the  interpretation  of  names 
that  Aristotle  seems  to  have  had  chiefly  in  view.  There 
is  another  phrase  also  sometimes  applied  to  the  same 
double  chance  of  eiTor ;  the  possibility  of  arguing  a  dicto 
simpliciter  ad  dictum  secundum  quid,  or  a  dicto  secun- 
dum quid  ad  d.ictuTn  sim^pliciter ;    and  perhaps  this 

supplies  the  more  really  descriptive  title. 
U 


294  FALLACIES.  [Pabt  IL 

Everything  that  can  be  named  may  be  viewed  as 
existing  at  once  simpliciter  and  secundum  quid  (or  as 
belonging  to  a  genus  and  also  possessing  a  difference). 
Everything  belongs  to  certain  classes,  the  narrower  *  of 
which  possess  difference  over  and  above  the  broader,  and 
beyond  the  narrowest  of  all  remains  any  real  individual 
peculiarity  of  the  thing  in  question.  Accordingly  any 
general  name  we  give  to  a  thing  neglects  of  necessity 
more  or  less  of  its  secundum  quid,  and  yet  in  order  to 
employ  deductive  proof  we  are  obliged  to  use  general 
(i.e.  significant,  or  indicating)  names.  S  may  be  rightly 
called  M,  but  it  is  also  always  something  more :  all 
depends  (as  we  have  seen  in  speaking  of  Analogy)  on 
whether  the  something  more  is  important  or  unimportant 
(essential  or  accidental)  for  the  purpose  in  hand. 

But  suppose  that  the  difference  is  ruled  unimportant 
and  that  M  is  decided  to  fairly  deserve  the  name  of  ^, 
that  name  in  turn  has  a  differential  and  a  generic  meaning, 
either  of  which  may  be  unduly  overlooked ;  and  so  on  for 
ever.  Take  the  name '  man.'  Because  a  man  is  certainly 
an  animal,  or  a  *  creature,'  or  even  a  '  thing,'  or  a  '  figure,' 
or  an  'object,'  we  do  not  thereby  gain  the  right  to  forget 
the  differential  qualities  due  to  his  human  nature:  nor 
on  the  other  hand  does  the  fact  of  his  rationality  do 
away  with  the  chain  that  binds  him  to  the  wider  class 
of '  animals,'  or  with  the  consequences  (such  as  mortality) 
therein  implied.     If  men,  through  developing  their  differ- 

♦  I.e.  narrower  by  direct  limitation,  not  merely  those  which  happen  to 
have  the  fewest  members. 


Chap.  Vt.]       THE  EMPLOYMENT  OF  GUESSWORK.  295 

entia  from  beasts  still  further,  should  eventually  manage 
to  conquer  death,  some  of  our  old  nomenclature  would 
require  remodelling,  but  the  logical  law  would  of  course 
remain  unaltered. 

The  traditional  examples  of  this  fallacy  are  valuable 
rather  as  being  unmistakable  than  as  reaUy  representative 
of  the  difficulty  involved.     "  You  are  not  a  man ;  for  a 
man  is  what  I  am,  and  you  are  not  what  I  am,"  or  "  You 
ate  raw  meat  to-day ;  for  you  bought  raw  meat  in  the  mar- 
ket yesterday,  and  to-day  you  ate  that  which  you  bought 
yesterday  in  the  market."     Practically  such  catches  as 
these  are  obvious  to  any  child,  and  in  order  to  exemplify 
the  working  of  the  real  danger  we  must  choose  a  finer 
shade  of  it.      For  this  purpose   the  best  examples  of 
neglecting  difference  are  perhaps  the  cases  where  some 
judgment  is  based  upon  what  may  be  called  a  partial  or 
one-sided  view  of  the  S :  where  the  name  with  which 
the  S  is  labelled  is  incompletely  defined,  defined  by  genus, 
without  the  full  differentia ;  as  where  a  soldier  is  said  to 
be  "  a  man  who  makes  a  contract  with  his  country  to  kill 
anybody  whom  his  country  wishes  to  have  killed."     In 
reality,  of  course,  the  soldier  does  not  make  this  contract 
simplidter,  but  there  are  other   elements  in  it,  which 
when  taken  into  account  may  perhaps  alter  radically  our 
opinion  of  his  merits.    Or  again,  voluntary  death  is  some- 
times heroic ;  and  suicide  is  certainly  always  voluntary 
death, — but  with  a  difference  added.     Voluntary  death  is 
the  genus  under  which  '  suicide '  comes,  but  the  specific 
difference  is  just  the   fact  that  the  motive  is  merely 


296  FALLACIES.  [Pabt  It 

to  escape,  for  ourselves,  something  which,  rightly  or 
wrongly,  we  regard  as  worse  than  death,  not  a  '  heroic ' 
thoughtlessness  for  ourselves  and  regard  for  the  good  of 
others. 

For  examples  of  neglecting  resemblance  we  may  take 
the  cases  where  difference  is  believed  to  be  thorough- 
going or  fundamental,  merely,  or  mainly,  from  the  fact 
of  different  names  being  used.  Readers  of  Newman's 
Grammar  of  Assent  will  remember,  for  instance,  the 
importance  there  given  to  the  difference  between  an 
assertion  and  a  conclusion.  The  two  names  are  different, 
and  the  two  things  are  certainly  so  far  different  that  an 
assertion  may  sometimes  be  made  "without  grounds," 
while  a  conclusion  (by  its  definition)  presupposes  grounds, 
weak  or  strong.  But  a  conclusion  means,  of  course,  an 
assertion  and  something  more :  it  belongs  to  the  genua 
assertion,  but  possesses  also  the  differentia  "  reasoned." 
Newman  indeed  prefers  to  say  (p.  2)  that  an  assertion  has 
"got  beyond  being  a  mere  conclusion,"  but  by  this  it 
appears  (p.  4)  he  means  merely  that  xmhesitating  faith 
is  stronger  than  faith  which  (p.  1)  consciously  depends  on 
a  prior  condition  being  true.  His  interest,  however,  is 
to  make  out  that  a  conclusion  is  radically  different  from 
(i.e.  does  not  even  belong  to  the  genus)  assertion,  and  for 
this  purpose  he  dwells  at  some  length  on  the  specific 
difference  (the  presence,  and  the  absence,  of  reference  to 
grounds).* 

*  It  shonld  be  mentioned,  however,  that  at  the  end  of  the  Bection 
(p.  6)  this  id  folt  to  be  hardly  safficient,  and  another  supposed  point  of 


CuAP.  VI.]       THE  EMPLOYMENT  OF  GUESSWORK.  297 

difference  has  to  be  bronght  forward,  resting  on  a  less  interesting  or 
important  verbal  confusion.  "  We  cannot  give  our  assent  to  the  proposi- 
that  *  X  is  y '  till  we  are  told  something  about  one  or  other  of  the  terms  " 
[I  should  rather  say,  both  the  terms]  ;  "  but  we  can  infer,  if  x  is  y,  and  y 
is  z,  that  X  is  z,'  whether  we  know  the  meaning  of  x  and  z  or  no."  The 
merest  beginner  in  logic  will  recognise  at  once  that  '  x  is  z '  does  not 
stand  here  for  a  single,  meaningless,  proposition,  but  merely  for  an 
indefinite  variety  of  possible  propositions  with  a  meaning.  All  that  is 
said  in  saying  that  in  such  a  case  we  recognise  the  reasoned  truth 
of '  x  is  z '  is  that  (with  these  premisses  admitted)  we  see  clearly  that 
X,  y,  and  z  may  mean  anything  whatever,  without  affecting  the  validity 
of  the  conclusion. 


CHAPTER  VII 

EEDUCTIO  AD  ABSUEDUM. 

Having  thus  spent  some  trouble  over  the  inquiry  what 
can  be  done  to  improve  our  methods  of  finding  ofi'hand 
the  source  or  cause  of  a  piece  of  faulty  reasoning,  it  is 
with  a  feeling  of  relief  that  we  now  turn  away  from  the 
difficulties  of  guesswork,  treading  again  upon  firmer 
ground.  Any  discussion  of  the  best  means  of  promptly 
discovering  the  actual  seat  of  a  fallacy  is  likely  to  raise 
more  difficulties  to  the  mind  of  the  thoughtful  reader 
than  it  can  settle  for  him.  He  will  feel,  at  the  end,  that 
educated  tact  and  insight  are  of  higher  value  for  such  a 
purpose  than  any  number  of  condensed  rules  can  be. 
The  special  circumstances  encountered  in  actual  argu- 
ments are  plainly  too  various  to  admit  of  hard  and  fast 
legislation,  and  the  most  that  can  be  hoped  is  that  some 
aid  may  have  been  given  in  clearing  away  preliminary 
confusion;  rendering  it  to  that  extent  more  easy  for 
further  small  advances  to  be  made.  But  now  there 
remains  the  question.  Where  guesswork  fails,  what  then  ? 
The  answer  has  been  briefly  given  already, — once,  and 


Chap.  VH.]  REDUCTIO  AD  ABSURDUM.  299 

directly,  on  p.  174,  and  on  other  occasions  (as  on  pp.  27, 
114,  213)  by  implication;  but  it  now  becomes  necessary 
to  deal  more  fully  with  it,  and  to  show  what  is  meant 
by  "applying  the  method  with  sufficient  fairness  and 
caution." 

The  Reduction  to  Absurdity,  it  was  also  said  above,  is 
a  method  of  raising  objections  which  is  ultimately  appli- 
cable in  all  cases  without  exception;  and  the  plans  of 
attack  already  hinted  at  are  only  to  be  preferred  to  it  on 
the  ground  of  their  greater  directness  in  certain  cases. 
It  should,  however,  be  at  once  explained  that  the  name 
'  Reduction  to  absurdity '  is  here  to  be  employed  in  a 
somewhat  narrower  sense  than  usual.  To  reduce  any 
assertion, — simple  assertion  or  argument, — to  absurdity 
is  always,  at  bottom,  to  bring  it  somehow  into  conflict 
with  observed  or  admitted  fact ;  and  this  may  of  course 
be  done  in  various  ways.  For  example,  to  produce  a 
contradictory  instance  might  fairly  be  called  a  mode  of 
reduction  to  absurdity :  or  again,  more  widely  still,  to 
bring  to  light  the  absurd  consequences  of  any  hypothesis. 
But,  as  applied  to  arguments,  rather  than  to  assertions 
in  general,  we  may  define  the  process  of  reducing  to 
absurdity  more  narrowly,  restricting  it  to  one  special 
method,  in  default  of  a  better  name  to  use  for  the  purpose. 
In  all  arguments  as  a  last  resource — and  in  some  even 
as  the  most  direct  attack — we  have  the  power  of  com- 
bining R  and  T,  inquiring  what  they  together  imply,  and 
then  comparing  such  further  assertion  with  observed  or 
admitted  facts.      For  simplicity  let  us  denote  "  required 


300  FALLACIES.  [Past  IL 

further  assertion**  in  every  case  by  the  letter  F;  then 
the  reduction  of  an  argument  to  absurdity  (as  the  name 
will  here  be  used)  means  the  objection  that,  T  and  E, 
being  given,  F  is  untrv£* 

The  fact  that  every  Thesis  deductively  proved, — every 
syllogistic  conclusion — rests  upon  some  law,  or  Prin- 
ciple, from  which  its  deduction  takes  place,  has  been 
already  sufficiently  noticed,  the  two  premisses  of  every 
Syllogism  being  respectively : — 

(1.)  The  major  premiss, — the  statement  of  such  law : 
and 

(2.)  The  minor  premiss, — the  application  of  it  to  the 
case  in  hand : 
and  whichever  of  these  be  given  as  R,  the  other  is  implied 
before  R's  'formal  adequacy'  is  complete.  But  now  it 
remains  to  be  said  that  every  R  must  be  translatable  into 
one  of  these, — ^major  or  minor  premiss, — before  we  can 
proceed  to  fully  test  the  argumentf  This  was  in  fact 
the  meaning  of  saying  that  all  Proof,  so  far  as  really 
Proof,  is  deductive,  and  that  the  Syllogism  is  "  perfectly 

*  It  must  be  noticed  that  F  is  not  contained  in  the  meaning  of  T 
and  B  together  in  the  same  way  exactly  as  T  is  contained  in  the  mean> 
ing  of  E  and  P;  but  it  is  as  truly  implied  by  them  nevertheless.  And 
if  that  which  T  and  R  together  imply  be  found  untrue,  the  argument  is 
clearly  overthrown :  for  B,  regarded  as  a  firm  support  for  T,  is  found  to 
require  as  true  a  proposition  which  is  in  fact  (or  by  admission) 
not  BO.  It  makes  no  difference  whether  F  be  Principle  or  Applica- 
tion: unless  both  of  these  are  true,  T  remains  without  the  required 
foundation. 

t  Hence  a  prior  condition  to  the  employment  of  the  method  is  agree- 
ment as  to  the  meaning  of  the  assertions  made  in  T  and  B. 


Chap.  VIL]  EEDUCTIO  AD  ABSUEDUM.  301 

general  in  its  operation :  applies  to  all  Proof  whatever, 
and  is  not  an  engine  to  be  used  in  deductive  inference 
merely."  That  is  to  say,  whenever  any  Reason  is  given 
for  any  Thesis,  a  knowledge  of  syllogistic  requirements 
will  enable  us  to  see  how  far  such  attempted  Proof  falls 
short  of  Demonstration ;  or,  in  other  words,  to  see  what 
further  assertion  must  in  every  case  be  added  to  R  before 
its  formal  adequacy  is  complete ; — ^before  all  has  been  done 
except  to  inquire  whether  R  is  true  in  fact.  Wherever 
any  Reason  is  given  for  any  Thesis,  and  the  special 
dangers  of  the  argument  are  not  immediately  apparent, 
hostile  criticism  faUs  back  at  once  on  the  inquiry.  What 
are  the  gaps  in  the  reasoning  that  possibly  require  to  be 
filled? 

The  Axiom  of  the  Syllogism,  whether  stated  in  *  ex- 
tension '  (i.e.  with  direct  reference  to  the  '  things '  spoken 
of),  in  the  famous  Dictum  de  omni  et  nullo, — which 
being  rendered  into  English  says  in  effect,  "  Whatever  is 
asserted  (affirmed  or  denied)  of  a  class  is  asserted  of  any 
part  of  that  class," — or  in  comprehension  (i.e.  with  direct 
reference  to  the  judgment  made)  in  the  equally  famous 
Nota  notce,  which  we  may  translate, — "  A  sign  (S)  of  a 
sign  (M)  of  ^,  itself  indicates  ^  " ; — the  Axiom  of  the 
Syllogism  requires,  for  purposes  of  Proof,  to  be  postu- 
lated true  in  its  'reciprocal'  form.  The  statement  so 
obtained  might  be  not  improperly  named  the  Dictum 
de  singulo  or  the  Nota  rei  ipsius.  It  says  that  in 
order  to  prove  anything  true  of  a  single  thing  (whether 
object,  quality,  event,  or  whatever  the  thing  may  be) 


302  FALLACIES.  [Part  IL 

it  must  also  be  shown  to  be  true  of  a  whole  class  of  such 
things,  a  class  including  the  one  observed.  Or,  stated  in 
comprehension, — In  order  to  prove  that  S  — >  ^,  S 
must  be  shown  to  indicate  M,  a  sign  of  ^. 

Let  no  one  think  these  postulates  either  a  valuable 
discovery  in  Logic,  or  an  unwarranted  and  presumptuous 
innovation.  They  are  merely  another  way  of  making 
the  familiar  assumption  that  "Nature  is  uniform/'  or 
that  there  are  'laws'  of  sequence  and  coexistence.  It 
is  on  this  assumption  that  all  explanation,  classification, 
and  prediction  necessarily  proceed.  Without  it  the 
Universe  would  be  a  chaos  of  exceptional  cases, — it 
'exceptions'  can  be  pictured  apart  from  'rules*  at  all. 
Every  individual  thing  represents  a  class,  of  which  it  is 
a  member;  everything  belongs  to  some  genus,  besides 
possessing  a  differentia.  Accordingly,  whenever  any  fact 
is  appealed  to  as  reason  for  believing  any  assertion,  the 
important  matter  is  to  get  the  supposed  underlying  law 
(or  laws)  clearly  stated;  and  the  central  difficulty  in- 
volved is  that  of  really  rising  above  the  individual  case 
while  at  the  same  time  avoiding  the  unfairness,  or  the 
pedantry,  of  insisting  that  a  wider,  and  therefore  more 
vulnerable,  law  is  implied  than  the  assertor  really  in- 
tends. It  is  true  that  E,  is  sometimes,  though  seldom, 
the  statement  of  the  law  itself, — as  in  the  argument  that 
"  Protective  duties  are  economical :  for  whatever  brings 
in  money  enriches : "  or  again,  "  The  farmers  will  not  pay 
in  rent  more  than  the  net  produce  of  their  farms,  for  no 
trading  class  will  continue  a  losing  business."     But  here 


Chap.  VII.]  REDUCTIO  AD  ABSURDUM.  303 

no  real  difficulty  can  arise,  except  through  verbal 
ambiguities,  and,  sometimes,  through  uncertainty  as  to 
the  Law  of  Counter-indication.  The  finding  of  the 
Application  when  the  Principle  is  clearly  expressed  must, 
from  the  nature  of  the  case,  be  always  an  easy  matter. 
Supposing  that,  in  the  first  of  the  two  instances  just 
given, — ^their  truth  or  cogency  does  not  interest  us  here, 
— "  enriches  "  and  "  are  economical "  are  used  in  the  same 
sense,  it  needs  no  Logic  to  tell  us,  at  this  stage  of  the 
work  at  least,  that  the  formal  adequacy  of  the  Reason 
depends  on  the  further  assertion  that  "  Protective  duties 
bring  in  money."  If  a  Principle  is  laid  down  as  Reason, 
even  a  child  can  seldom  fail  to  see  that  its  force  as 
Reason  depends  on  its  being  connected,  in  the  only  way 
possible,  with  the  Subject  of  the  Thesis.  Of  course  there 
are  cases  conceivable,  where,  through  accepting  the  reci- 
procal as  equivalent,  a  wrong  application  may  be  made. 
But  this  danger  has  been  already  sufficiently  discussed. 
We  need  not  here  go  back  to  the  pons  asinorurrh  of 
Logic. 

We  have  to  deal,  then,  solely  with  the  case  where  R, 
if  relevant  at  aU,  is  not  itself  the  Principle,  but  is  either 
(1)  directly,  or  (2)  remotely,  the  Application.  By  a 
'  remote '  Application  isr  meant  the  case  (briefly  referred 
to  on  p,  210)  where  the  S  of  the  thesis  is  not  expressly 
mentioned  by  the  Reason.  But  first  of  the  case  where 
the  Application  given  is  as  direct  as  possible.  That  is, 
where  something  is  distinctly  said  about  S  as  a  reason 
for  believing  the  assertion  made  of  it ;  as  in  '  Gold  can- 


304  FALLACIES.  [Pabt  U. 

not  be  produced  artificially,  for  it  is  an  elementary  sub- 
stance/ or  '  Whales  are  not  fishes,  for  they  breathe  by 
lungs,'  or  '  He  must  be  in  London,  for  he  is  not  at  his 
country  house.* 

The  whole  difiiculty  here  is  as  to  the  extent  of  the 
Principle  really  involved.  Is  it,  for  example, '  To  be  an 
element  — >  incapability  of  artificial  production,*  'To 
breathe  by  lungs  — >  not  to  be  a  fish '  (the  counter 
equivalent  of  'To  be  a  fish  — >  not  to  breathe  by 
lungs  '),  *  Not  to  be  at  one's  country  house  — >  to  be  in 
London*  (i.e.  'All  who  are  not  at  their  country  houses 
are  in  London  *) ;  or  is  it  the  narrower  assertions, '  Gold, 
if  an  elementary  substance  — >  incapability  of,  etc.,' 
*  Breathing  by  lungs,  when  found  along  with  the  other 
attributes  of  a  whale  — >  non-fish,'  'If  he  is  not  at  his 
country  house,  he  must  be  in  London '  ?  The  answer  to 
this  question  furnishes  the  key  to  the  distinction  between 
fair  and  unfair  employment  of  the  method  for  reducing 
to  absurdity.  The  difierence  between  what  Logic  might 
be,  and  what  it  too  often  is  (what  perhaps  its  less  thought- 
ful enemies  suppose  it  always  to  be),  is  much  like  the 
difierence  between  fair  and  unfair  caricature  :  a  difference 
not  so  much  in  the  thing  itself  as  in  the  manner  in 
which  it  is  interpreted,  and  the  occasions  on  which  it  is 
employed.  It  is  chiefly  the  inability  to  keep  this  dis- 
tinction clear  which  has  made  it  possible  for  orators  to 
describe  the  Syllogism  as  "a  contrivance  for  catching 
you  in  a  trap  and  holding  you  fast  in  it." 

Just  as  the  middle  term  in  a  Syllogism  (the  term 


Chap.  Vn.]  EEDUCTIO  AD  ABSURDUM.  305 

appearing  in  both  premisses)  may  always  be  viewed  as  a 
sign,  or  mark,  possessed  by  S, — a  mark  which,  abstractly 
indicating  (or  being  a  universal  sign  of)  ^,  is  employed 
to  prove  the  conclusion;  so,  conversely,  that  which  is 
asserted  by  R  as  indicated  (abstractly  or  concretely)  by 
S,  may  always  be  viewed  as  the  middle  term  of  a  Syllo- 
gism which  has  yet  to  be  completed.  If  S  is  only  known 
to  be  ^  because  it  is  M,  M  is  (according  to  the  Dictum 
de  singulo)  thereby  asserted  to  be  universally  a  sign 
of  ^.  If  S  is  only  known  to  be  ^  because,  beiing  If, 
it  is  M,  M,  when  specially  limited  in  this  manner  by 
N,  is  thereby  asserted  to  be  universally  a  sign  of  ^.* 
The  proposition  MN  — >  ^  is  of  course  just  as  truly 
'  universal '  as  M  — >  §^,  though  of  narrower  sweep. 

Are  we  then,  whenever  we  meet,  put  forward  as 
Reason  for  any  Thesis,  a  minor  premiss  which  is  bare  of 
special  limitation,  to  assume  that  no  special  limitation 
was  present  to  the  mind  of  the  person  so  putting  it  for- 
ward ?  Yes,  and  No.  For  the  purpose  of  getting  the 
principle  expressly  defined,  it  is  often  highly  desirable  to 
assume,  provisionally  and  fictitiously,  that  the  wide  Prin- 
ciple, as  strictly  implied  by  the  reasoning,  was  believed 
to  be  true.  By  this  means  wavering  imcertainty  as  to 
its  falsehood  may  often  be  destroyed,  and  even  where  no 
shade  of  such  hesitation  existed  it  is  a  clear  gain  to  get 
the  real  principle  reduced  to  definiteness.  But  if  we  go 
beyond  this  employment  of  the  method,  we  ourselves 

*  E.g.  '  S  is  guilty  (S)  ;  since,  (N)  thongb  the  cbarge  is  one  that  an 
innocent  person  would  readily  contradict,  it  has  (M)  never  yet  been 
expressly  contradicted.' 


•306  FALLACIES.  [Part  II. 

commit  probably  the  greater  error  of  the  two.  Thus 
while  no  objection  would  perhaps  be  raised  to  demanding, 
as  Principle  for  'Gold  cannot  be  produced  artificially, 
since  it  is  an  element,'  the  assertion  that  '  all  elements 
are  incapable  of  artificial  production,'  it  is  obviously  un- 
fair to  demand  as  the  Principle  strictly  involved  by  '  He 
must  be  in  London,  since  he  is  not  at  his  country  house,' 
the  assertion  that  'All  who  are  not  at  their  country 
houses' — stiU  less  'All  who  are  not  at  his  country 
house ' — '  are  in  London,'  thus  neglecting  the  fact  that 
other  alternative  places  of  residence  exist.  The  absur- 
dity, if  we  made  such  a  demand,  would  rather  lie  with 
ourselves.  In  such  a  case  as  this,  since  there  could  not 
be  any  hesitation  as  to  the  suggested  Principle  being  im- 
true,  we  should  probably  dispense  with  even  the  ficti- 
tious and  provisional  assumption  of  it,  cutting  the  process 
short  by  asking  at  once  what  the  special  circumstances 
are  which  are  supposed  to  limit  him  (not  '  all  men ')  to 
one  place  or  the  other.  But  there  are  plenty  of  really 
doubtful  cases.  Take  fui-ther  the  argument  'He  must 
be  ill :  for  he  has  lost  his  appetite.'  Here  the  principle 
really  believed  as  foundation  might  be  that  'loss  of 
appetite  universally  indicates  illness ; '  or,  on  the  other 
hand,  it  might  be  merely  '  if  he  has  lost  his  appetite  he 
must  indeed  be  ill,' — the  special  circumstance  thereby 
indirectly  hinted  being  of  course  that  S's  appetite  is 
known  to  be  of  a  particularly  unfailing  kind.  If  the 
latter  were  the  true  explanation,  we  should  of  course 
make  a  grave  mistake  in  attempting  to  lay  upon  the 


Chap.  VII.]  REDUCTIO  AD  ABSURDUM.  307 

assertor  the  burden  of  supporting  the  truth  of  the  wider 
assertion;  but  we  should  be  quite  right  in  giving  him 
the  choice  between  doing  so  and  narrowing  it  down  into 
a  shape  that  will  fit  the  facts. 

The  method  of  reducing  to  absurdity  should,  then,  be 
regarded  rather  as  a  method  of  putting  questions  than  of 
making  a  direct  assertion  that  an  absurdity  is  necessarily 
implied.  We  can  never  really  get  so  far  behind  the 
scenes  of  another  person's  mind  as  to  attain  complete 
security  in  guessing  what  the  exact  Principle  relied  upon 
has  been.  We  can  only  say  that  the  Principle  which 
appears  to  tus  to  be  implied  by  the  express  statement  is 
so  and  so,  and  that  we  presume  he  hardly  intends,  in 
fact,  to  rely  on  any  such  plain  absurdity.  He  must 
either  narrow  it  for  our  benefit,  or  be  content  to  leave  us 
unconvinced :  we  certainly  cannot  accept  the  argument 
as  it  stands.  So  far  as  the  Principle  fails  to  attain  some 
generality  wider  than  the  T  itself,  so  far  the  T  remains 
unrationalised, — i.e.  without  a  logical  foundation :  so  far 
as  the  principle  sacrifices  security  for  the  sake  of  gene- 
ralisation, so  far  the  foundation  is  unsound.  We  do  not 
catch  the  assertor  in  a  trap :  we  merely  show  him  that 
he  has  chosen  to  place  himself  in  a  dilemma :  and  we 
then  request  him,  for  our  enlightenment,  to  choose  which- 
ever alternative  he  himself  prefers.  If  for  any  reason  he 
does  not  like  to  rationalise  his  thesis  by  committing  him- 
self to  any  definite  Principle,  it  is  always  open  to  him  to 
be  content  to  leave  us  unconvinced. 

But  there  is  a   sense  in  which  this  may  be  called 


308  FALLACIES.  [Pabt  IL 

stating  the  alternatives  a  little  too  baldly.  In  a  certain 
sense  there  may  be  a  flaw  in  our  conviction,  and  yet  not 
a  serious  chasm.  There  is  a  middle  ground  between 
complete  Demonstration  and  total  failure  to  justify  belief. 
There  are,  in  a  sense,  different  shades  of  certainty; 
evidence  varies  in  strength.  Where  we  cannot  get  an 
assertion  completely  demonstrated  from  a  definite  and 
faultless  principle,  the  next  best  thing  is  to  demand  that 
the  Principle  shall,  if  vague,  be  as  unexceptionable  as 
possible ;  if  sound,  as  simple  as  possible ;  and  that  we 
shall  know,  even  incompletely,  what  the  Principle  really 
is,  and  to  what  extent  it  may  be  trusted.  Knowledge, 
even  when  in  the  empirical  stage,  is  often  better  for 
practical  purposes  than  pure  ignorance  would  be.  And 
this  leads  us  to  speak  of  the  sole  remaining  case, — where 
the  Reason  is  '  remotely '  the  Application. 

When,  for  example,  I  argue  by  Analogy,  and  equally 
when  I  base  a  law  on  facts  observed,  nothing  at  aU  is 
said  in  the  Keason  about  precisely  the  S  of  the  Thesis. 
In  the  former  kind  of  argument,  as  already  seen,  the 
Reason  speaks  of  a  supposed  '  parallel  case ; '  in  the  latter 
kind,  of '  This  (or  these)  S '  only,  not  of  '  All  S '  as  in  the 
Thesis.  So  again  in  such  (very  common)  deductive  argu- 
ments as  '  A  storm  is  brewing,  for  the  glass  has  fallen 
rapidly,'  or  '  My  friend  is  out,  for  there  is  no  light  in 
his  window ; '  here  the  respective  theses  speak  of  '  a 
storm '  and  *  my  friend,'  while  the  Reasons  speak  of '  the 
glass,'  and  *a  light  in  the  window.'  In  perhaps  the 
majority  of  actual  arguments  we  cannot  say,  without 


Chap.  VIL]  EEDUCTIO  AD  ABSURDUM.  309 

great  circumlocution,*  that  the  S  of  the  Thesis  is  directly 
spoken  of  by  the  Reason,  and  in  the  process  of  translating 
into  and  out  of  the  clumsy  phrases  required  for  doing 
so,  there  are  endless  opportunities  for  verbal  error  to 
creep  in. 

In  the  analogical  and  the  inductive  arguments,  it  is 
probably  in  most  cases  the  simplest  plan  to  try  directly 
for  unsuspected  and  essential  difference;  but  there  can 
be  no  harm  in  pointing  out  the  longer  method  of 
arriving  at  the  further  assertion  involved.  The  com- 
pletely definite  underlying  Principle  differs  radically 
in  the  two  cases  (Analogy  and  Induction),  being  alike 
only  in  the  one  point  of  being  often  highly  complicated 
and  extremely  difficult  to  state  with  any  exactness.  In 
the  argument  from  analogy  the  S  of  the  Principle 
implied  is  the  inventory  of  the  (often  vaguely  felt  and 
numerous)  points  of  essential  resemblance  between  the 
two  parallel  cases :  these  points  of  resemblance  are  im- 
plied by  the  argument  to  indicate  Z,  either  universally 
or  at  least  indifferently  in  the  two  cases  before  us.  In 
the  inductive  argument  the  fuU  underlying  Principle 
is  the  statement  that  certain  precautions  in  observation 
or  experiment  are  sufficient  to  warrant  the  inference. 
These,  it  must  be  confessed,  are  nearly  always  too 
numerous  for  concise  summation.  In  the  presence  of 
the  almost  infinite  diversity  of  the  circumstances  in 
which  observation  and  experiment  may  take  place,  we 

*  Cf.  Jevons,  Elementary  Lessons,  p.  164. — "  The  circumstances  of 
the  barometer  falling  are  the  circumstances  of  bad  weather  coming." 


310  FALLACIES.  [Pabt  IL 

have  not  yet  got  far  towards  generalising  the  sufficient 
safeguards.  Mill's  five  methods  were  an  attempt  in  this 
direction,  but,  as  we  have  seen,  it  is  only  as  ideals  that 
they  are  satisfactory,  and  the  point  of  practical  import- 
ance is  always  to  know  how  near  to  the  ideal  the  given 
experiment  approaches ;  for  which  piece  of  '  special ' 
knowledge  an  enlightened  review  of  innumerable  cir- 
cumstances, and  of  their  bearing  on  the  case,  is  needed. 

But  if  we  cannot  in  these  cases  arrive  at  any  full 
and  definite  statement  of  the  Principle,  still  the  method 
of  reducing  to  absurdity  may  be  of  service  in  another 
way.  Whatever  be  the  S  of  Thesis  or  of  Reason,  the 
truth  of  the  Reason  as  a  whole  is  given  as  indicating 
that  of  the  Thesis,  and  consequently  (by  counter-indi- 
cation) the  untruth  of  the  Thesis  as  indicating  that  of 
the  Reason.  In  other  words,  it  is  always  asserted  that 
were  the  Thesis  untrue,  the  Reason  would  he  untrue 
also  :  and  this,  if  the  Reason  be  given  as  true,  is  clearly 
absurd.  In  other  words  again,  every  argument  asserts 
that  no  theory  except  the  thesis  is  compatible  with  the 
reason.  In  yet  other  words,  that  all  possible  rival 
theories  have  been  examined  and  found  wanting. 

Here  we  touch  again  upon  the  difficulties  surrounding 
the  burden  of  Proof.  This  last  statement  may  at  first 
almost  appear  as  if,  after  all — to  quote  a  former  passage 
(p.  149) "  the  sole  concern  of  the  assertor  were  to  frustrate, 
^one  by  one,  attempts  at  disproof  made  by  the  other 
side."  The  real  case  is  however  very  difierent.  Until 
he  has  shown  that  all  such  attempts  are  worthless,  he 


Chap.  VII.]  EEDUCTIO  AD  ABSURDUM.  311 

may  have  an  underlying  Principle  indeed,  but  it  must 
be  one  whose  material  truth  has  not  yet  passed  our 
examination.  In  proportion  to  the  extent  of  rival  theory 
still  remaining  undestroyed,  is  the  weakness  of  the  evi- 
dence brought  forward.  Often  these  rival  theories  may 
all  be  summed  up  in  one  concise  expression,  and  may  in 
this  shape  be  discarded  en  bloc.  Thus  in  the  analogical 
argument  we  may  say  that  there  was  perhaps  'some 
cause '  for  ^  being  Z,  which  cause  is  inoperative  in  the 
case  of  S.  That  is  to  say,  if  the  assertor  can  show  some 
probability  to  the  contrary,  he  has  done  more  to  support 
his  assertion  than  if  such  alternative  has  never  occurred 
to  him  or  has  been  half-consciously  suppressed  as  in- 
convenient. So  in  the  inductive  argument  we  may  sum 
up  the  alternatives  by  saying  that  perhaps  the  law  is 
stated  too  widely,  and  here  again  there  are  ways  of 
showing  what  has  been  done  to  limit  its  sweep  as  care- 
fully as  possible :  and  also  ways  of  letting  out  the  secret 
that  we  have  gladly  caught  at  the  first  explanation,  and 
afterwards  obstinately  refused  to  see  its  obvious  faults. 

In  this  employment,  however,  of  the  Reduction  to 
Absurdity,  as  well  as  in  the  easier  case  first  noticed,  the 
attitude  of  fair  investigation  is  still  the  same.  The 
essential  characteristic  of  it  is  that  it  avoids  dogmatic 
assertion,  and  merely  asks  to  see  what  has  really  been 
done  to  stop  the  gaps  in  the  reasoning  or  to  minimise 
the  opportunities  of  error.  It  is  noteworthy  that  in  other 
matters  also  the  same  negative,  anti-dogmatic  tendency 
has  always  been  observable  in  Logic.    Even  when  Logic 


312  FALLACIES.  [Pabt  H. 

undertook  to  interpret  to  some  extent  the  meaning  of 
words  and  phrases  off-hand,  we  find  at  least  a  strong 
inclination  to  bind  them  down  to  the  least  amount  of 
positive  assertion  which  the  words  could  be  supposed 
to  contain.  '  Some '  meant  '  not-none  '  instead  of  '  some 
only;'  the  universal  affirmative  could  not  by  itself  be 
taken  to  express  reciprocal  indication ;  the  Principle  of 
Logical  Division  treats  A  and  not-A  as  equal  in  import- 
ance; and  quite  recently  we  have  had,  in  Mr.  Venn's 
Symbolic  Logic,  a  more  consistent  following  out  of  the 
plan  of  interpreting  statements  merely  by  what  they 
deny,  than  had  ever  before  been  openly  and  distinctly 
attempted.  Logic  is  in  far  more  danger  of  losing  its 
operative  power  in  hesitation  and  inactivity  through 
extreme  desire  for  fairness,  than  of  lending  any  aid  to 
unfair  quibbling,  or  of  trying  ingeniously  to  make  the 
worse  appear  the  better  reason. 

An  additional  circumstance,  another  straw  helping 
to  show  the  direction  in  which  the  current  of  Logic 
sets,  may  be  found  in  the  fact  that  so  often  its  enemies 
are  merely  talkers  who  dislike  the  check  that  reason 
always  gives  to  ready  dogmatism;  reasoners  who  care 
more  to  do  their  reasoning  easily  than  correctly,  or  who 
have  not  yet  become  aware  that  any  great  need  for 
caution  exists.  It  is  chiefly  because  they  lack  the  calm- 
ness and  strength  required  for  looking  difficulties  in 
the  face,  and  because  Logic  contents  itself  with  asking 
whether  they  have  1-eally  done  so,  that  they  dislike  its 
methods.    I  do  not  mean,  however,  that  the  wish  to 


Chap.  VII]  REDUCTIO  AD  ABSURDUM.  313 

assert  without  foundation  is  the  only  explanation  of  all 
possible  objections  to  Logic,  and  before  quitting  the 
subject  it  may  be  worth  while  even  briefly  to  notice 
some  of  the  more  disturbing  things  that  can  be  genuinely 
urged  against  the  science.  As  already  sufficiently  ex- 
plained, however,  I  can  here  attempt  to  notice  only  those 
objections  that  may  arise  before  Philosophy, — as  cut 
loose  from  all  merely  practical  considerations, — is  brought 
to  bear  upon  the  question. 


CHAPTER  VIIL 

SOME  OBJECTIONS   TO  LOGIC. 

The  practical  objections  to  Logic,  other  than  those  merely 
felt  without  the  trouble  of  thought  or  inquiry,  seem  to 
me  broadly  divisible  into  two  groups :  those  which  claim 
that  the  logical  attitude  is  on  the  whole  useless,  or 
worse ;  as  for  instance  that,  consistently  held,  it  means 
pure  stagnation  or  scepticism,  and  that  even  a  partly 
inconsistent  holding  of  it  is  apt  to  leave  us  too  long 
undecided :  and  those  which  admit  that  the  end  is  good, 
but  declare  that  the  means  are  clumsy. 

The  former  of  these  is  certainly  the  more  serious 
of  the  two,  and,  as  said  above,  I  can  in  fact  only  provide 
a  half-satisfactory  answer.  It  seems  impossible  to  deny 
that  even  our  most  careful  reasoning  may  lead  us  into 
mistaken  views ;  and  strictly  speaking,  the  more  we  re- 
cognise this  fact,  the  less  room  must  there  be  for  active 
faith. 

But  it  is  one  thing,  after  all,  to  admit  the  fact  and 
quite  another  to  admit  the  hasty  inference  sometimes 
drawn  from  it.      It  is  not  true  that  because  every  sup- 


CuAP.  VIIL]  SOME  OBJECTIONS  TO   LOGIC.  315 

posed  fact  is  ultimately  uncertain,  therefore  there  is  no 
useful  distinction  to  be  made  between  a  careful  induc- 
tion and  a  hasty  guess.  There  are  endless  shades  of 
difference  here,  and  nothing  is  gained,  except  the 
cheapest  sort  of  peace  of  mind,  by  shutting  our  eyes 
to  them.  If  there  are,  strictly  speaking,  no  degrees  in 
fallibility,  yet  there  are  differences  of  the  highest  im- 
portance between  the  results  of  care  and  carelessness  in 
reasoning.  It  is  for  the  most  part  mere  sloth,  or  even 
sometimes  a  kind  of  pettishness,  that  leads  us  to  resolve 
to  reason  carelessly  because  with  all  possible  care  we 
may  still  make  mistakes.  Perhaps,  indeed,  it  will  be 
said  that  no  one  ever  really  "resolves  to  reason  care- 
lessly," and  this  may  be  granted  at  once.  The  pro- 
cess is  commonly  described  in  finer  language.  It  is 
"  humility,"  not  slackness  of  purpose,  that  prevents  our 
asserting  positively  that  black  does  not  mean  white. 
It  is  "in  a  spirit  invincibly  calm"  (nor  can  I  quarrel 
with  the  epithet)  that  we  claim  a  vision  of  "  loftier  than 
mere  material  verities  and  wider  than  purely  physical 
laws."  Or  we  contradict  ourselves,  and  then  call  the 
result  a  "  Mystery,"  or  an  "  Antinomy  of  Reason,"  wash- 
ing our  hands  of  all  responsibility,  and  content  to  lay  it 
on  the  Powers  that  designed  the  faulty  human  intellect. 
The  humble  mind  has  an  easy  command  of  numerous 
humble  phrases.  / 

Practically  the  surest  defence  against  Scepticism  lies, 
pot  in  claiming  infallible  revelations,  but  in  patiently 
making  the  best  of  the  truths  that  have  stood  the  test 


316  FALLACIES.  [Pabt  II. 

of  time.  Not,  of  course,  only  the  few  that  exist  now  in 
the  shape  in  which  they  were  originally  put  forward,  but 
also  the  many  that  have  been  gradually  narrowed  down 
and  pared  into  lasting  shape  by  persistent  hostile  forces. 
On  these  we  'ancients'  build,  as  on  a  basis  always 
growing  firmer : — though  in  recognising  the  fact,  we  of 
course  admit  that  our  basis  is  never  completely  firm. 
But  just  in  this  recognition  lies  the  life  and  strength  of 
science ;  for  the  admission  gives  a  power  to  discover  and 
correct  mistakes,  and  also  tends  to  weaken  the  natural 
petty  desire  to  pose  as  supernaturally  knowing.  Free 
from  the  fear  of  being  found  an  impostor,  science  is 
able  to  challenge — and  to  court — correction:  more  than 
it  loses  in  influence  by  being  proved  mistaken,  it  gains 
by  being  known  as  honest,  and  it  adds  a  further  gain  by 
registering  the  mistake.  Knowledge  is  built  upon  a  mass 
of  prejudices,  possibly,  bnt  one  difierence  between  scientific 
and  unscientific  prejudices  is  that  the  former  are  chiefly 
recognised  as  provisional  merely.  If  it  were  not  for 
these  strong  provisional  prejudices,  Science  would  hardly 
have  reached  the  results  already  won.  UntU  they  prac- 
tically fail  these  may  be  trusted,  and  where  they  are 
proved  in  any  case  fallacious  we  only  learn  a  further 
piece  of  knowledge,  and  so  really  add  to,  not  weaken, 
our  old  foundations.  Logic  is  fond  enough  of  reminding 
us  that  "All  men  are  fallible:"  but  the  rider  must  be 
added  that  it  depends  largely  on  ourselves  to  say  to 
■what  extent  we  choose  to  live  under  the  sway  of  fallacy. 
And  as  to  unpractical  hesitation,  again  we  may  appeal 


Chap.  VIU.]  SOME  OBJECTIONS  TO  LOGIC.  317 

to  results.  It  is  easy  of  course  to  assert  that  these  have 
been  reached  by  Common  Sense  in  spite  of  Logic,  and  in 
one  sense  possibly  this  may  be  true.  But  that  is  an 
objection  to  a  name,  and  not  to  a  process :  whether 
'  logic '  or  not,  it  is  consistency  of  thought,  deep  analysis 
of  supposed  simple  phenomena,  and  recognition  of  possible 
unknown  antecedents,  to  which  the  results  have  been 
mainly  due.  To  refuse  all  belief  until  we  reach  absolute 
demonstration  would  of  course  be  an  unpractical  habit ; 
but  between  doing  this  and  merely  recognising  the 
possible  loopholes  of  error,  there  is  all  the  difference  that 
exists  between  standing  still  and  moving  cautiously. 

It  is  clear  too  that  these  more  fundamental  objections 
to  careful  inquiry  would  come  with  greater  force  if  they 
were  once  for  all  to  declare  their  exact  position  unmis- 
takably. At  present  they  are  apt  to  shift  their  ground 
too  fast  to  hold  it  firmly.  Science  finds  itself  between 
two  apparently  contradictory  objections,  both  often 
coming  from  the  same  objector,^ — that  it  is  too  dogmatic, 
and  also  not  dogmatic  enough.  Either  on  the  whole,  or 
on  any  given  point,  one  or  other  of  these  charges  may  be 
true ;  but  it  would  at  least  tend  to  enable  us  to  correct 
our  errors,  if  the  charges  were  to  cease  to  destroy  each 
other. 

A  more  insidious  form  that  this  objection  to  Logic, 
and  defence  of  Fallacy,  sometimes  takes,  closely  resem- 
bles the  attitude  of  loose,  good-humoured  Optimism 
towards  the  problem  of  Evil.    Since  Fallacy  is  a  fact  in 

Nature,  let  us  recognise  it  as  part  of  the  wisely-ordered 
15 


318  FALLACIES.  [Past  II. 

scheme  of  things,  without  which  Nature  would  be  'in- 
complete.' To  hold  it  merely  for  an  enemy  is  '  narrow ' 
and  'one-sided.'  Or  let  us  view  it,  at  the  lowest,  as 
useful  manure  to  raise  the  crops  of  reason.  Nearly  all  the 
more  important  theories  we  possess  have  been  preceded 
by  a  number  of  false  ones,  and  without  the  latter  the 
former  could  never  have  been  attained.  Only  the  slug- 
gard never  commits  a  fallacy.  A  touch  of  madness  is 
usually  found  along  with  the  highest  genius,  and  no  one 
is  good  for  much  who  lacks  a  spice  of  the  fool. 

This  is,  of  course,  an  unduly  brief  account  of  the  view 
here  spoken  of;  and  it  is  eminently  a  view  that  will 
hardly  bear  so  definitely  stating,  but  needs  as  much  dilu- 
tion as  possible.  Perhaps,  however,  it  will  serve  to  show 
what  is  intended,  more  especially  as  the  statement  given 
above  does  mix  up — ^just  as  the  easy  optimists  commonly 
do — two  quite  distinct,  and  mutually  destructive,  de- 
fences, neither  of  which  would  be  found  so  satisfactory 
by  itself.  The  first  of  these, — that  Fallacy  is  a  part  of 
our  total  nature,  and  therefore  worthy  of  our  respect, 
rests  on  a  merely  verbal  confusion,  and  one  which  no 
man  has  ever  yet  quite  been  able  to  preserve  consistently. 
If  Fallacy  is  a  part  of  our  nature,  so,  surely,  is  the  power 
to  recognise  Fallacy  as  luiprofitable,  and  the  wish  to 
avoid  it  as  far  as  we  can.  There  is  hardly  any  element 
of  human  nature  really  stronger  than  the  wish  to  dis- 
criminate between  truth  and  error, — except  perhaps  the 
wish  to  keep  the  still  wider  distinction  of  good  and  evil 
clear.     While  we  are  about  worshipping  our  instincts. 


GiiAP.  VIIL]  SOME  OBJECTIONS  TO   LOGIC.  319 

why  neglect  the  most  fruitful  and  persistent  of  them  all  ? 
That  the  view  has  a  certain  charm,  over  and  above  the 
mere  refreshing  effect  of  the  paradox,  will  be  readily 
admitted  by  most  people.  It  is  often  a  great  relief,  and 
sometimes  has  a  healing  and  strengthening  effect,  to  feel 
free  to  relax  our  wakefulness  a  little.  But  the  thing  can 
be  very  easily  pushed  over  into  an  absurdity, — or,  what 
is  worse,  can  be  accepted  as  a  serious  theory  by  minds 
that  might  otherwise  have  kept  or  attained  some  vigour. 
To  yield  to  it  to  any  great  extent  is  as  enfeebling  to  the 
mind  as  long-continued  sensuous  luxury  to  the  body : 
the  comfortable  sentiment,  "  I  am  sufficient  as  I  am," 
may  be  of  use  now  and  then  as  a  piece  of  rather  open 
self-deception,  but  a  mind  that  truly  and  firmly  held  such 
belief  for  any  considerable  length  of  time  would  miss  the 
bracing  effect  of  a  struggle  for  improvement. 

The  second  defence, — that  error  often  leads  to  truth, 
— has  this  advantage  over  the  first,  that  it  does  preserve 
the  distinction  between  the  preferable  and  the  unprefer- 
able.  And  so  long  as  this  is  clearly  and  consistently 
done,  I  do  not  see  that  we  need  at  all  object  to  recognise 
the  fact.  But  this  is  certainly  no  argument  for  remaining 
in  an  error  longer  than  we  can  help.  By  all  means  admit 
that  liability  to  error  is  part  of  the  price  we  have  to 
pay  for  forward  movement ;  but  are  we  to  pay  the  price 
and  then  contentedly  forget  to  carry  home  the  purchase  ? 
The  transaction  needs  again  to  be  viewed  from  both  sides 
instead  of  from  one  only.  Rather  than  stop  short  at  the 
fact  that  fallacy  has  its  uses,  we  need  to  remember  that 


320  FALLACIES.  [Paet  IT. 

it  is  only  justifiable  when  it  has  really  led  to  the  good 
results;  and  this  is  apt  to  be  sometimes  forgotten. 
There  is,  however,  one  purpose  for  which  the  view  in 
question  seems  to  me  to  have  considerable  value,  and  that 
is,  to  force  us  to  see  that  a  man  who  commits  even  a 
large  number  of  fallacies  is  by  no  means  necessarily  a 
fooL  I  do  not  mean  that  this  is  an  advantage  only  so 
far  as  it  leads  us  into  charity  towards  opponents,  but 
also,  and  chiefly,  that  it  tends  to  weaken  the  weight  of 
mere  authority  as  regards  any  given  question:  a  man 
may  have  all  the  wisdom  and  learning  of  an  Aristotle,  and 
yet  be  quite  mistaken  on  a  given  important  point.  The 
recognition  of  this  fact  tends  to  make  us  value  conclusions 
more  on  their  own  merits  and  less  on  the  merits  of  those 
who  advance  them. 

Such,  in  rough  outline,  are  the  chief  objections  of 
this  class.  On  the  whole,  I  think  we  may  say,  that  when 
viewed  as  mere  protests  against  the  opposite  extreme, 
they  often  have  a  value.  But  they  are  too  seductive  in 
themselves,  too  gratifying  to  common  vanity,  and  too 
open  to  employment  as  simple  excuses  for  idleness,  to 
remain  always  in  their  proper  place,  and  as  a  rule  their 
professed  exponents  appear  by  no  means  conscious  of 
the  needed  limitations. 

As  regards  the  objection  that  Logic  is  too  slow  and 
clumsy  to  be  of  the  highest  practical  service,  there  seems 
little  to  be  said,  except  to  admit  the  fact,  and  even 
to  urge  it  as  a  reason  for  doing  all  we  can  to  improve 
the  methods   of  fighting  fallacy.     It  seems  imdeniable 


Chap.  VIII.]  SOME  OBJECTIONS  TO  LOGIC.  321 

that  there  is  an  artificial  rigidity  about  all  definition,  a 
false  simplicity  about  analysis,  a  standing  failure  in  all 
attempts  to  cram  the  universe  into  labelled  nutshells. 
Where  Proof  depends  on  many  intricate  special  circum- 
stances taken  together,  the  analytical  habit  of  mind  may 
often  be  disastrous.  There  are  plenty  of  valuable 
facts  too  shadowy  for  Proof,  and  plenty  of  occasions 
where,  if  we  had  to  wait  for  logical  investigation,  the 
opportunity  would  be  gone, — "there  being,"  as  Bishop 
Warburton  expressed  it,  "  no  worse  practical  men  than 
those  who  require  more  evidence  than  is  necessary."  If 
common  sense  is  rough.  Logic,  at  least,  is  far  from  ready, 
and  sometimes  its  pretended  deeper  insight  is  practically 
either  futile  or  misleading :  for  Logic  is  bound  by 
language,  and  language  always  hangs  a  little  behind 
the  newest  glimpses  of  truth. 

The  facts  being  admitted,  it  is  much  easier  to  find 
this  fault  with  any  existing  system  of  Logic  than  to 
supply  a  better  system :  and  if  the  objection  were 
brought  solely,  or  mainly,  by  those  who  know  something 
of  the  difficulties  to  be  encountered,  every  one  who  cares 
about  the  matter  would  welcome  it  gladly.  Unfortu- 
nately this  cannot  be  said  to  be  the  case.  The  alterna- 
tive everyivhere  suggested  by  these  objectors  is  one 
which  growing  experience  has  always  been  steadily 
finding,  on  the  whole,  untrustworthy.  Whether  we  call 
the  alternative  '  common  sense '  or  '  intuition,'  its  fault 
is  the  same, — that,  where  it  really  exists,  it  is  so  truly 
a  better  instmment  than  slow  and   deliberate  reason. 


322  FALLACIES.  [Pakt  II. 

that  people  are  apt  to  claim,  or  to  imagine,  they 
possess  it,  when  they  really  possess  it  not.  It  is  open  to 
any  lunatic  to  know  by  intuition  that  he  is  the  angel 
Gabriel,  just  as  it  was  formerly  open  to  common  sense  to 
see  that  the  Sun  went  round  the  Earth,  or  to  feel  that 
the  Antipodes  were  a  plain  absurdity. 

In  the  face  of  omnipresent  illusion,  and  of  possible 
lunacy,  it  seems  that  we  must  often  be  content  to  sacri- 
fice speed,  at  least,  in  the  attempt  to  get  the  most  objective 
standard  possible.  Whether  breadth  of  view  need  really 
be  sacrificed  depends  chiefly  on  the  time  at  disposal  in  the 
given  case,  partly  also  on  our  power  of  employing  highly 
general  words  or  symbols.  But  what  is  here  contended 
is,  that  whatever  be  the  sacrifice  required,  it  is  safer  to 
make  it  than  to  imagine  the  other  alternative  reallj'^  pre- 
ferable on  the  whole.  It  is  not  claimed  that  whenever  we 
are  called  upon  to  reason  we  shall  gain  by  deliberately 
reducing  the  process  to  formulas.  But  what  is  claimed 
is  that  unless  we  have  the  power  to  do  so,  we  have 
nothing  else  to  keep  our  reasonings  straight.  There  are 
two  distinguishable  states  of  mind  in  which  slow  and 
deliberate  reasoning  is  now  and  then  dispensed  with, — 
one  the  reasoned  belief  that  in  a  given  case,  or  set  of 
cases,  it  is  better  to  trust  to  rapid  insight,  doing  this, 
however,  with  all  the  care  available  and  with  a  clear 
recognition  of  the  danger ;  and  the  other,  the  far  com- 
moner state  of  mind,  composed  partly  of  mere  easy-going 
ignorance  of  the  difficulties,  partly  of  dim  and  floating 
views  of  important  truths,  and  largely  perhaps  dependent 


Chap.  Vm.]  SOME  OBJECTIONS  TO  LOGIC.  823 

on  more  purely  physical  conditions.  These  are,  at  least, 
the  two  ends  of  the  scale  :  no  one  is,  quite  consistently, 
either  an  angel  or  a  fool,  either  a  doubter  or  a  seer; 
and  even  the  man  who  follows  his  '  moods '  has  a 
reasoning  mood  amongst  others.  But  still  we  may  class 
men  broadly  in  two  opposite  camps,  according  as,  on  the 
whole,  they  are  for  or  against  the  deliberate  use  of 
reason.  In  the  former  case,  we  occasionally  make  a 
compromise  and  voluntarily  accept  what  seems  to  us 
in  the  special  instance  the  smaller  of  two  evils ;  in  the 
latter  case, — and  hence,  no  doubt,  its  popularity, — we 
know  little  or  nothing  of  evils  or  of  danger,  but 
merely  glow  with  faith  in  our  penetration,  and  with 
honest  anger  at  any  attempt  to  call  the  results  in 
question.  If,  as  so  often  happens  in  the  latter  case,  we  are 
also  gifted  with  eloquence,  it  lies  in  our  power  to  do 
much  harm  to  those  who  have  not  yet  declared  for  either 
side.  It  is  easy  enough  to  paint  Insight  in  florid  and 
striking  colours,  Reason  as  cold  and  dismal:  and  the 
weaker  brethren  are  always  glad  of  a  powerfully  phrased 
excuse. 

There  is,  no  doubt,  much  to  be  said  against  the 
careful  employment  of  reason;  but  it  is  not  the  whole 
story,  nor  even  the  most  important  part  of  it.  The 
practical  problem  is,  how  to  make  use  of  logic  without 
spoiling  our  common  sense,  or  how  to  make  use  of  our 
common  sense  with  rather  less  common  discretion.  Im- 
patience with  logical  method  may  no  doubt  here  and 
there  be  justified,  whether  in  Philosophy  or  in  looser 


324l  FALLACIES,  [Pabt  IL 

regions  of  thought ;  but  far  more  often  it  is  merely  an 
expression  of  the  unchecked  desire  to  run  before  we 
have  learnt  to  walk.  Here  and  there  it  is  plain  that  the 
impatience  springs  from  a  genuine  wish  for  improve- 
ment in  our  methods,  but  far  more  often  it  flows  either 
from  idleness  or  from  being  unaware  that  there  are 
any  methods  to  improve.  And  in  any  case,  though  we 
may  appreciate  the  good  intention  shown,  as  yet  the 
fruits  are  wanting.  If  logical  method  as  at  present 
known  is  insufficient,  the  sole  alternative  is  unmethodic 
speculation,  which  on  the  whole  is  less  sufficient  still. 
It  is  open  to  any  one  to  sit  down  and  dream  that  to  him 
alone  has  been  given  the  key  of  all  knowledge — or  of 
any  given  piece  of  knowledge, — ^without  any  laborious 
precautions.  And  perhaps  he  may  be  right.  But  how 
is  he,  after  all,  to  be  sure  of  this  on  reflection,  and 
how  are  his  friends  to  know  it,  and  the  other  people 
with  different  dreams  of  their  own  ?  Whether  the  seer 
needs  an  objective  standard  or  not,  he  will  hardly  deny 
that  rival  seers  need  one  :  and  in  their  case,  at  least,  he 
finds,  just  as  the  scoffers  do,  that  the  calm  security  of 
inspiration  is  difficult  to  distinguish  from  a  child's 
untroubled  conceit. 


CONCLUSION. 

SUMMARY. 

To  challenge  attack  is  of  the  essence  of  *  real  *  assertion, 
and  the  kind  of  challenge  depends  on  the  confidence 
with  which  the  assertion  is  made.  Sometimes  we  speak 
as  having  fully  considered  the  question ;  sometimes  as 
rather  waiting  to  hear,  as  a  novelty,  what  may  be  said 
on  the  other  side.  It  is  with  the  former  case  only  that 
we  have  been  here  concerned,  and  for  convenience  in 
describing  this  kind  of  assertion  we  have  employed  the 
ancient  name  of  Thesis. 

The  first  of  the  dangers  that  a  Thesis  has  to  run,  we 
found  to  be  that  of  containing  the  empty  form  of  asser- 
tion without  the  substance.  If  no  real  meaning  be 
understood  by  the  hearer,  to  him  the  thesis  is  non- 
existent, whether  for  acceptance  or  attack.  And  the 
hearer  alone  can  decide  how  far  the  meaning  is  real. 

When  the  meaning  is  real  and  clear — or  sufficiently 
clear  for  its  purpose — the  second  danger  is  that  of  sup- 
posing that  a  thesis,  to  be  left  imaccepted,  stands  in  need 
of  Disproof.     And  here  the  distinction  between  Disbelief 


326  FALLACIES.  [Pabt  IL 

and  Unbelief  is  all-important :  or,  however  the  states  of 
mind  be  named,  the  thing  to  remember  is  that  so  long  as 
a  thesis  is  unsupported  it  has  not  yet  been  shown  to  be 
either  true  or  false ;  that  although  it  claims  to  be  true,  its 
claim  is  not  yet  made  out.  The  attempt  to  support  an 
assertion  by  asking  what  can  be  said  against  it,  may  be 
met  by  replying  that  at  present  we  know  nothing  against 
it,  but  this  much  against  accepting  it — that  we  see  no 
reason  to  believe.  He  who  asserts  may  choose  between 
the  two  alternatives — producing  reasons  to  satisfy  the 
inquirer,  or  leaving  him  unconvinced. 

And  lastly,  when  reasons  are  brought  forward,  the 
question  at  once  arises,  how  far  the  proof  comes  short  of 
being  conclusive  :  or  what  are  the  gaps  remaining  before 
Demonstration  is  complete.  And  having  found  these  (as 
they  appear  to  the  inquirer),  the  safe  and  fair  attack  is 
still  to  ask  for  information  :  not  necessarily  to  accuse  the 
assertor  of  absurdity ;  only  to  force  him  to  take  care  that 
he  in  fact  avoids  it. 

But  to  view  the  office  of  Logic  as  consisting  purely  in 
sceptical  attack,  is  itself  a  kind  of  artifice,  undertaken 
with  a  far  more  useful  purpose  in  view.  It  is  not  the 
seizing  of  firm  positions  in  verbal  controversy  that  is  the 
chief  aim  of  logical  method,  but  the  power  thus  gained 
may  be  used  as  a  means  to  a  further  end.  Since  a  priori 
any  belief  may  be  erroneous,  and  especially  since  we 
have  already  often  found  ourselves  and  others  mistaken, 
there  is  a  certain  use  in  learning  to  treat  ourselves  as  the 
wary  debater  would  treat  a  less  wary  opponent.     The 


Conclusion.]  SUMMARY.  327 

attack  on  any  erroneous  belief  must  come  either  before 
or  after  its  acceptance  has  led  us  into  actual  error.  The 
practical  purpose  of  Logic  is  to  enable  us  to  forestall  the 
possible  attacks,  and  so  to  guard  against  the  consequences 
of  credulity.  Logic  thus  aims  at  the  adoption  only  of 
those  beliefs  that  cannot  fairly  be  avoided,  and  its  opera- 
tion ia  in  the  fii-st  place  mainly  to  restrict  the  natural 
exuberance  of  belief. 

It  is  not  necessary  here  to  repeat  in  any  completeness 
of  detail  all  the  separate  points  of  doctrine  on  which  the 
science  of  Logic  depends :  nor  can  I,  indeed,  pretend  to 
be  able  to  sum  them  up  in  the  most  concise  available 
form.  Apart  from  metaphysical  difficulties,  the  latter 
operation  would  demand  both  a  wider  symbolic  language 
than  is  at  present  accepted,  and  also  a  more  universal 
practice  of  handling  symbols  easily  and  reading  their 
application.  Expressed  in  more  highly  general  language 
than  we  have,  the  logical  doctrines  that  are  of  chief 
importance  from  the  practical  point  of  view  would  prob- 
ably be  few  in  number,  simple  in  nature,  far-reaching  in 
their  application,  and  true  under  all  conditions  of  their 
use.  Such  as  we  have  already  are,  when  wrongly  inter- 
preted, open  of  course  to  easy  caricature — as  every  pun  and 
every  verbal  puzzle  bears  witness :  but,  interpreted  fairly, 
we  need  never  be  afraid  of  trusting  our  weight  upon 
them.  Like  Science  in  general.  Logic  exists  for  a  pur- 
pose, and  wherever  it  fails  to  attain  that  purpose  the 
failure  merely  needs  incorporation  into  our  statement  of 
its  laws.     Thus  we  may  use,  for  example,  the  law  of  Con- 


328  TALLACIES.  IPabt  II. 

tradiction,  while  fully  admitting  that  the  line  between  A 
and  not-A  is  a  contrivance  of  our  own :  or  we  may  use 
the  Reduction  to  Absurdity  while  recognising  that  it  only 
asks  a  question.  But  without  attempting  here  to  draw 
up  the  list  of  doctrines,  it  may  be  of  use  to  select  as  land- 
marks for  memory  some  of  the  salient  features  of  the 
science. 

The  first  of  these  I  hold  to  be  the  negative  attitude 
above  spoken  of.  And  the  second,  all  that  is  included 
under  the  name  Consistency.  As  already  shown,  this 
contains  much  more  than  what  is  commonly  meant  by 
*  abiding  by  our  assertions,'  namely  the  whole  problem  of 
bringing  to  light  the  hidden  implications  underlying  a 
thesis,  and  especially  the  large  assertion  implied  in  every 
confident  theory — that  all  possible  conflicting  theories  are 
to  be  discarded.  That  this  demand,  if  strictly  enforced, 
would  be  a  bar  to  all  belief,  may  be  freely  admitted. 
What  Logic  is  concerned  to  do  is,  not  to  remove  all 
theoretical  doubts,  but  to  force  us  into  recognising  as 
clearly  as  possible  their  actual  extent  and  power  in  the 
given  case.  As  a  first  means  of  pointing  out  the  dangers, 
it  sets  up  an  ideal  type  of  Demonstration,  and  then 
demands  not  that  we  shall  reach  this  but  that  we  shall 
know  clearly  how  far  short  of  it  we  fall:  for  it  finds 
that  until  the  distinction  between  proven  and  not-proven 
is  apprehended  with  some  real  distinctness,  there  is  no 
chance  of  dealing  successfully  with  the  endless  complica- 
tions due  to  varying  degrees  of  strength  in  evidence. 
The  more  we  inquire  into  the  main  sources  of  error,  the 


CoNCJLisiON.]  SUMMARY.  329 

more  clearly  we  see  that  ignorance  of  danger  is  at  once 
the  commonest  and  the  only  one  that  we  can  certainly 
remove.  Hence  the  central  purpose,  for  practice,  is  to 
find  the  gaps  in  Proof  remaining  to  be  filled. 

The  definable  term,  the  abstract  proposition,  and  the 
argument,  have  this  in  common,  that  each  is  capable  of 
being  viewed  as  expressing  an  indication.  Given  the 
general  name,  and  any  of  the  essential  attributes  follow ; 
given  the  S  of  an  abstract  proposition,  and  the  ^  follows ; 
given  the  Reason  and  the  Thesis  follows.  And  to  each 
of  the  three  the  rule  of  counter-indication  applies :  deny 
an  essential  attribute  and  we  deny  the  name ;  deny  ^ 
and  we  deny  S;  deny  the  Thesis  and  the  relevant 
Reason  is  denied. 

In  the  attainment  of  Consistency  the  Law  of  counter- 
indication  has  two  chief  uses  ;  first  that  of  restraining  us 
from  taking  two  distinct  assertions  as  equivalent,  and 
secondly  as  a  means  of  helping  to  bring  to  light  the 
hidden  implications.  In  the  former,  or  negative,  aspect 
it  operates  chiefly  by  preventing  us  from  proving  some 
easy  proposition  under  the  belief  that  we  thereby  prove 
its  reciprocal  also.  In  the  positive  aspect  the  chief  value 
of  the  law  is  in  helping  to  explain  the  syllogistic  process. 
But  such  explanation  demands — 

Next,  the  assumption  that  every  isolated  fact  comes 
under  a  wider  law.  This  doctrine  lies  at  the  root  of 
Proof  and  of  Explanation  equally.  To  prove  a  thesis, 
we  need  to  show  it  as  a  case  under  some  Principle — 
just  as,  to  explain  a  name  we  have  to  mention  a  genus. 


330  FALLACIES.  [Part  IL 

or  as  to  explain  a  fact  we  have  to  bring  it  under  a  law. 
And  of  that  Principle  the  thesis  may  be  either  a  denial 
of  the  antecedent  (S),  or  an  affirmation  of  the  consequent 
(^)  •  while  the  Reason  either  denies  the  consequent  or 
affirms  the  antecedent.  By  means  of  Thesis  and  Reason 
together  we  can  thus  find  the  law  implied. 

Lastly,  there  is  the  doctrine  that  every  isolated  fact 
is  further  analysable — that  besides  belonging  to  a  genus, 
it  possesses  also  a  specific  difference.  And  that,  in  order 
to  view  such  fact  correctly  we  need  to  bear  its  differential 
qualities  in  mind.  The  eye  for  genus  thus  leads  us  to 
attempt  to  establish  our  thesis  deductively,  while  the 
eye  for  differentia  becomes  the  main  safeguard  of 
induction.  While,  then,  we  continue  to  assume,  as 
a  basis  for  practical  proof,  that  all  '  things '  belong 
to  classes,  the  names  of  which  may  be  used  as  in- 
dicating certain  facts  about  them.  Inductive  Logic 
teaches  us  to  cultivate  the  eye  for  difference, — to  keep 
refining  away  what  passed  at  first  sight  as  indivisible, 
and  breaking  down  ancient  barriers  that  perhaps  have 
served  some  useful  purpose  but  were  better  suited  to 
clumsier  needs  than  ours.  Deductive  Logic  insists  that 
conclusiveness  depends  on  indication, — the  trustworthi- 
ness of  laws ;  inductive  Logic  leads  us  to  revise  the  laws 
themselves,  and  put  us  on  guard  against  accepting  them 
too  widely.  The  power  of  seeing  finer  shades  of  differ- 
ence is  on  the  whole  the  best  and  most  lasting  result 
of  logical  training,  and  affords  most  help  in  the  rapid 
detection  of  fallacy. 


Conclusion.]  SUMMARY.  331 

These  seem  to  be,  in  briefest  outline,  the  more  im- 
portant points  to  keep  in  mind :  but  as  thus  shortly 
stated  they  can  only  be  of  use  as  memoranda,  not  as  in 
themselves  by  any  means  sufficient  statements  of  all  that 
is  required  for  practice.  Nor,  certainly,  would  such 
sufficient  statements  be  easy  to  frame.  It  is  not  theory 
alone  that  can  ever  fully  enable  us  to  preserve  the  golden 
mean  between  faith  and  hesitation.  So  commonly  is 
this  fact  recognised,  however,  that  it  will  be  well 
if  we  can  avoid  going  far  beyond  it  and  accept- 
ing the  easy  view  that  Theory  and  Practice  must 
for  ever  carry  on  a  hopeless  warfare,  and  that,  so 
often  as  our  weak  attempts  at  theory  fail  to  fit 
the  facts,  it  is  sufficient  to  plead  the  possession  of  a 
highly  practical  spirit.  Perhaps  one  chief  source  of 
difficulty  here  is  the  habit  of  supposing  that  Logic  wishes 
to  dictate  instructions  for  belief, — saying,  for  example, 
"This  you  may  consider  sufficiently  certain,  but  that 
you  shall  not  accept."  No  logic  can  really  lay  claim  to 
so  supreme  an  authority.  It  is  wiser  to  admit  that  men 
are  perfectly  free  to  form  their  beliefs,  if  they  choose, 
with  the  aid  even  of  self-deception.  The  most  that  Logic 
can  hope  to  do,  for  practice,  is  to  help  us  to  know  the 
dangers  of  uncriticised  belief;  it  is  entirely  our  own 
concern  if  we  afterwards  prefer,  in  a  given  case,  to  disre- 
gard them.  The  risks  however  remain,  whether  we  care 
to  remember  them  or  not. 


APPENDIX. 

A.* 

ALTERNATIVE  POSSIBILITIES. 

As  a  help  in  recognising  the  alternative  theories  against 
which  any  abstract  proposition  has  to  show  its  preferability, 
there  may  be  some  use  in  setting  out  the  a  joriori  possibilities 
between  S  and  ^  in  general. 

We  must  remember  that  S  and  gk  are  abstracted  portions 
of  the  total  phenomena  among  which  they  respectively  occur; 
portions  selected  and  named  by  ourselves,  for  the  purposes 
of  our  '  general  knowledge : '  the  actual  phenomena  observed 
being  complex  wholes,  mentally  analysable  into  this  that 
and  the  other  circumstance,  whether  such  circumstances  be 
events  or  qualities.  It  should  be  observed,  however,  that 
when  successive  phenomena  are  in  question  these  abstracted 
portions  may  always  themselves  be  viewed  as  '  events,'  even 
where  so  uneventful  as  hardly  to  deserve  the  name  in  popular 
language.  Thus,  where  any  quality  of  any  thing  changes 
ever  so  slightly, — say  when  a  thermometer  rises  one  degree, 
— we  have  what  is  here  considered  an  '  event,'  even  though 
a  caterer  for  news  might  hardly  think  it  worth  reporting. 
And  the  abstractness  of  such  an  event  consists,  as  abstract- 
•  See  p.  276. 


334j  appendix. 

ness  always  consists,  in  its  detachment  from  surronnclings : 
we  choose  to  keep  out  of  our  assertion  (and  as  far  as  possible, 
out  of  sight)  the  whole  environment  of  S  and  of  <^,  and  to 
speak  of  these  alone,  labelling  them  with  general  names. 
For  example,  let  S  be  a  rise  in  the  price  of  coals,  and  ^ 
a  strike  among  the  colliers.  Outside  S  and  <§,  and  simul- 
taneous with  them,  is  a  whole  universe  of  other  events 
and  qualities,  too  numerous  to  sum  up  by  any  narrower 
expression  than  their  '  environment : '  these  we,  by  a  sort  of 
fiction,  choose  to  neglect,  attending  only  to  S  and  ^. 

And  first,  when  S  is  observed  to  happen  earlier  in  time 
than  5 ;  if  we  inquire  as  to  the  various  ways  in  which  these 
may  conceivably  be  related  to  each  other  in  Causation,  we 
find  :— 

First  S  may  be  cause  of  5  '• — 

(1)  as  what  is  often  loosely  called  the  sole  cause.  That 
is,  if  S  had  not  happened,  5  would  not  have 
happened;  all  other  circumstances  in  S's  environ- 
ment being  '  accidental '  to  5 :  as  where  S  is  the 
passing  of  a  bullet  through  a  healthy  man's  brain, 
and  5  the  death  of  the  man. 

(2)  S  and  a  third  circumstance,  Z,  may  have  been 
jointly  essential  to  <5's  happening.  That  is,  without 
their  combination,  <§  would  not  have  happened :  as 
where  Z  is  a  certain  person's  weak  state  of  health,  S 
is  the  arrival  of  fever-infection,  and  ^  his  consequent 
fever. 

(3)  S  and  Z  may  have  jointly  contributed  to  .S's  ex- 
istence, without  their  combination  being  essential  to 
the  production  of  <^  at  all.  That  is,  without  one  of 
them,  5  might  have  happened,  but  not  to  so  great  an 
extent  or  intensity :  as  where  S  and  Z  are  a  pair  of 
horses,  and  ^  the  movement  of  the  carriage. 


ALTERNATIVE  POSSIBILITIES.  335 

(4)  S  may  have  been  itself  due  to  a  former  case  of  5, 
but  may  now  be  in  its  turn  cause  (whether  sole  or 
otherwise)  of  the  piesent  ^ :  as  where  S  is  a  rise  in 
the  bank-rate,  and  ^  a  general  uneasiness  in  the 
money-market. 

Secondly,  S  and  ^  may  be  co-effects  of  Z :  as  where  S  is 
day,  5  is  night,  and  Z  is  the  earth's  revolution  in 
the  sunlight :  or  where  Z  is  a  '  centre  of  depression,' 
S  is  a  falling  barometer,  and  ^  a  storm. 

Tliirdly,  7i  may  have  been  (sole  or  other)  cause  of  <^,  and 
S  accidental: — 

(1)  Simply  accidental,  as  where  S  is  the  act  of  blowing, 
^  is  the  flying  open  of  the  watch-case,  and  Z  is  the 
pressure  of  my  finger  on  the  spring.  (Along  with 
this  may  be  classed  the  case  where  Zis  the  effect  of 
S,  and  5  accidental :  as  where  S  is  the  arrival  of  a 
comet,  Z  a  letter  in  the  Times  about  it,  and  <Sb  a 
war.) 

(2)  Z  may  have  been  the  cause  of  5,  and  S  a  hindrance : 
as  where  <§  is  the  flourishing  state  of  trade  in 
America,  Z  is  the  'boundless  resources  of  the 
country,'  and  S  is  the  system  of  Protective  Duties. 

Looking  next  at  the  case  of  Co-existence,  we  shall  find  in 
the  first  place  that  unless  S  and  5  stand  merely  for  qualities 
(or  groups  of  qualities),  and  not  for  events,  it  will  be  very 
difficult  to  find  examples  of  true  co-existence  with  direct 
dependence  between  S  and  Jb-  In  other  words,  where  S  and 
5  are  two  co-existent  events,  say  where  S  is  the  arrival  of  a 
train  at  the  station,  and  ^  the  arrival  of  the  clock's  hands 
at  a  certain  position ;  or  where  S  is  a  gale  and  ^  the  move- 
ment of  the  branches  of  a  tree ;  the  case  is  always  more  or 
less  plainly  resolvable  either  into  one  of  co-effects,  or  else  of 
innumerable   repeated  acts  of  causal  sequence.    As  to  co- 


336  APPENDIX. 

efiFects;  if  it  be  true  that  every  event  whose  beginning  we 
can  trace  has  had  a  cause,  and  also  that  any  selected  portion 
of  continuous  Nature  that  we  choose  to  consider  separately 
may  be  bound  up  into  a  single  '  event,'  it  is  clear  that  the 
relation  itself  of  co-existence  between  S  and  5b  may  be  con- 
sidered as  an  event,  and  therefore  as  having  a  cause.  And 
thus,  unless  the  whole  assumption  on  which  our  explanation 
of  Nature  proceeds  be  unfounded,  every  case  of  co-existence 
is,  strictly  speaking,  a  case  of  co-effects.  We  have  only  to 
trace  back  the  chain  of  causation  far  enough,  and  sooner  or 
later  we  must  come  to  an  ancestral  event  common  to  both. 
But  this  fact,  however  undeniable,  is  of  small  practical  value, 
since  the  interests  of  practice  require  above  all  things  a  dis- 
tinction between  the  cases  where  S  and  ^  are  essential  to 
each  other  and  where  they  are  accidental.  And  the  sweeping 
general  assertion  made  above  cannot  be  held  to  deny  the 
apparent  (and  therefore  practically  existent)  disconnection 
between  many  cases  of  observed  co-existence.  The  falling  of 
a  cab-horse  in  Cheapside  may  co-exist  with  a  particular 
storm  at  Penzance  (to  go  no  further  afield),  and  if  we  knew 
all  the  links  no  doubt  we  should  be  able  to  trace  both  events 
back  to  some  ancestral  cause,  however  inconceivably  exten- 
sive and  complex.  The  horse,  let  us  say,  would  not  have 
fallen  unless  the  street  had  been  wet,  and  tliis  occurred 
because  certain  rain  drops  had  come  down  in  that  par- 
ticular place  and  time :  the  falling  of  the  rain  depended 
on  certain  atmospheric  collocations  and  changes,  and  these 
again  on  others  in  an  endless  series  where  we  soon  lose  all 
actual  clue.  But  our  whole  theory  of  causation  demands 
that  at  some  time  or  other  in  the  past,  however  remote,  a 
change,  or  group  of  changes,  took  place,  to  which  both 
the  Penzance  storm  and  the  Cheapside  accident  are  due, 
— without    which    neither    would  have   happened   exactly 


ALTERNATIVE  POSSIBILITIES.  337 

as  and  when  they  did  happen.  This  seems  certainly 
demanded  as  a  theoretical  assumption :  and  yet,  for  all 
practical  purposes,  the  two  events  in  question  were  '  totally 
disconnected,'  Just  as,  practically,  there  is  such  a  thing  as 
*  Chance,'  so  must  we  admit  that  many  cases  of  co-existence 
are  '  purely  accidental,'  or  '  mere  coincidences ; '  even  if  this 
means  only  that  we  have  no  definite  knowledge  of  the  actual 
chain  of  causation  involved. 

And  as  regards  the  case  of  innumerable  repeated  acts  of 
causal  sequence, — as  where,  for  instance,  a  stream  runs  on  for 
ages  and  slowly  polishes  a  rock, — the  flow  of  the  water  may 
be  said,  in  rough  ordinary  language,  to  co-exist  with  the 
wearing  of  the  stone,  but  the  process  can  also  easily  be 
analysed  into  infinitesimal  acts  of  removal  of  particles  by 
abrasion, — the  eflect  in  each  case  coming  after  its  cause  in 
time.  In  fact,  in  one  sense,  any  other  explanation  is  incon- 
ceivable. Here  again  we  have  a  case  where  theoretical 
assumptions  clash  with  tlie  practical  needs  of  expression; 
and  where,  as  it  seems,  our  only  resource  is  to  yield  to  the 
latter.  "While  admitting  then  that,  strictly  interpreted, 
co-existence  is  only  of  qualities,  which  are  always  co-efiFects 
of  some  prior  cause;  we  must  be  content  with  a  looser 
form  of  expression,  and  speak  of  co-existent  events  also, 
one  of  which  may  be  either  essential  or  accidental  to  the 
other. 

Of  co-existent  events  then,  the  conceivable  cases  follow 
closely  the  division  above  made  of  successive  events, 
namely : — 

First,  either  may  be  the  cause  of  the  other : — 

(1)  Sole  cause ;  e.g.  S  the  forward  movement  of  a  train 

and  5  the  rotation  of  the  wheels. 

(2)  Joint  essential ;  e.g.  S  the  force  of  Gravity,  Sb  the 

fall  of  an  apple,  and  Z  the  absence  of  support. 


338  APPENDIX. 

(3)  Joint  contributing  ;  e.g.  S  a  large  river,*  5  a  large 

town  upon  the  river,  and  Z  the  other  causes  of  the 
size  of  the  town. 

(4)  Reactive ;  e.g.  S  reason,  and  5>  language. 
Secondly,  S  and  ^  may  be  co-effects  of  Z.     E.g.  S  a  low 

thermometer,  5>  the  formation  of  ice,  and  Z  frosty  air. 
Thirdly,  the  conjunction  of  S  and  ^  may  be  '  purely  acci- 
dental '  {i.e.  S  the  effect  of  Z,  and  ^  of  X.) 

(1)  Simply  ;  e.g.  S  fine  weather  and  ^  Eoj^al  review. 

(2)  Obstructively ;  (either  existing  in  spite  of  the  other). 

E.g.  S  liberty  of  the  press,  and  ^  the  spread  of 
foolish  theories. 
Of  co-existent  qualities,  only  three  cases  need  be  distin- 
guished : — 

(1)  S  and  ^  essential  f  to  each  other.    (This  case  is  rare.) 

E.g.  S  inertia,  and  ^  weight. 

(2)  5  essential  f  to  S. 

E.g.  S  human  nature,  and  Sb  fallibility. 

(3)  ^  accidental  to  S. 

(a)  Simply; 

E.g.  S  shortsightedness  and  ^  short  stature. 
()S)  Obstructively. 

E.g.  S  disregard  of  wealth,  and  ^  possession  of 

wealth.^ 

Seeing  then  that  when  events  or  qualities  are  observed  to 

happen  in  succession  or  co-existence,  there  are  a  priori  these 

various  explanations  possible,  how  are  we  to  rise  from  the 

*  It  may  seem  strange  to  call  a  iai"ge  river  or  a  large  town  'events,' 
biit  here  the  names  are  only  used  elliptically,  for  the  growth  of  the  town 
and  the  continued  existence  of  the  river ;  so  too  in  the  other  cases. 

f  By  *  essential '  is  here  meant  no  more  than  '  constantly  accom- 
panying,' and  therefore  '  indicated.' 

X  This  further  exemplifies  the  difficulty  noticed  on  p.  335,  that 
causation  is  sometimes  so  subtle  as  to  wear  the  appearance  of  co- 
existence. 


THE  EMPIRICAL  METHODS  IN  DETAIL.  339 

observations  or  experiments  made,  to  the  law  of  succession  or 
co-existence  obtaining  between  the  things  ?  I  do  not  mean, 
by  what  method  are  we  to  direct  our  guesses  so  as  to  be 
most  quickly  successful ;  but  how,  having  made  a  theory,  are 
we  to  prove  it  ? 

It  will  be  seen,  of  course,  that  these  alternatives  just  set 
out  are  alternatives  which  affect  our  explanation  of  each 
single  observed  case  of  sequence  or  co-existence.  But  since, 
in  order  to  prove  a  concrete  proposition  satisfactorily  we 
must  always  have  at  least  one  abstract  proposition  to  rely 
upon,  the  whole  importance  of  these  alternatives  is  as  regards 
the  proof  of  abstract  propositions  from  concrete  facts  observed. 
Before  considering  a  law  established,  either  by  one  or  by 
many  cases  of  observed  sequence  or  co-existence,  these  alter- 
natives have  to  be  faced,  as  possible  explanations  of  each 
case  observed.  And  the  immediate  question  in  each  case  is, 
What  certainty  can  we  obtain  that  the  alternative  chosen  is 
the  right  one  out  of  all  those  conceivable  ?  The  methods  of 
inductive  proof  may  be  viewed  as  attempts  to  answer  this 
question. 

B  * 

THE  EMPIRICAL  METHODS  IN  DETAIL. 

As  Mill  pointed  out,  the  five  methods — Agreement,  Joint- 
Method,  Difference,  Eesidues,  and  Concomitant  Variations 
— exemplify  at  bottom  two  methods  only.  Agreement  and 
Difference,  the  Joint  Method  being  merely  an  extension 
and  improvement  of  the  Method  of  Agreement,  the  Method 
of  Residues  being  a  peculiar  modification  of  the  Method  of 
Difference,  and  the  Method  of  Concomitant  Variations  being 

•  See  p.  278. 


340  APPENDIX. 

an  approach  to  the  Method  of  Difference,  the  nearest  approach 
attainable  in  certain  circumstances.  There  are,  then,  two  main 
axioms  at  the  foundation  of  all  the  methods ;  the  first,  that 
whatever  circumstances  can  be  excluded  without  excluding 
the  phenomenon  whose  effect  (or  cause)  is  being  sought,  or 
can  be  absent  notwithstanding  its  presence,  are  not  causally 
connected  with  it.  According  to  this  rule,  accidental  circum- 
stances are  gradually  eliminated  by  observation,  and  the  more 
observations  the  greater  the  chance  that  the  truly  accidental 
circumstances  will  be  excluded.  The  remainder,  those  cir- 
cumstances which  are  not  eliminated  by  this  process,  are 
supposed  to  be  thus  shown  to  be  essential  to  the  phenomenon, 
to  be  the  proved  effect  (or  cause).  As  a  concise  example,  we 
may  quote  from  Professor  Fowler, "  A  particular  kind  of  food, 
whatever  else  I  may  eat  or  drink,  and  however  vaiious  my 
general  state  of  health,  the  temperature  of  the  air,  the 
climate  in  which  I  am  living,  and  my  divers  other  surround- 
ings, invariably  makes  me  ill,"  [let  us  say  rather  '  is  invari- 
ably followed  by  my  illness  ']  ;  "I  am  justified  in  regarding 
it  as  the  probable  cause  of  my  illness,  and  avoid  it  accord- 
ingly." Here  the  general  state  of  health,  the  temperature, 
and  the  other  surroundings,  are  the  circumstances  gradually 
eliminated,  by  the  observations,  as  immaterial;  and  it  is 
supposed  that  the  only  circumstance  (except  an  uncertain 
number  of  circumstances  already  believed  to  be  immaterial) 
common  to  all  the  instances  observed,  and  thus  surviving 
the  process  of  elimination,  is  the  '  particular  kind  of  food.' 
So  far,  then,  as  the  method  of  agreement  is  to  be  trusted,  this 
particular  food  is  proved  to  be  the  cause.  We  may  guarantee, 
says  the  Method  of  Agreement,  by  means  of  the  observed 
facts,  the  abstract  propo>ition,  "  This  particular  kind  of  food  ' 
(S),  whenever  taken,  indicates  future  illness  in  me  (<S)." 

The  second  axiom,  on  which  the  Methods  of  Difference, 


THE  EMPIRICAL  METHODS  IN  DETAIL.  341 

direct  and  supplementary,  are  based,  admits  of  a  two-sided 
statement :  "  Whatever  antecedent  cannot  be  excluded  with- 
out preventing  the  phenomenon,  is  the  cause,  or  a  condition, 
of  that  phenomenon :  whatever  consequent  can  be  excluded, 
with  no  other  difference  in  the  antecedent  than  the  absence 
of  a  particular  one,  is  the  effect  of  that  one."  *  Chemistry  is 
one  of  the  best  fields  for  illustration  of  this  method.  "  Mix, 
for  example,"  says  Prof.  Fowler,  "  chloride  of  mercury  with 
iodide  of  potassium,  and  the  result  will  be  a  colourless  liquid 
at  the  top  of  the  vessel,  with  a  brilliant  red  precipitate  at  the 
bottom.  There  can  be  no  hesitation  in  ascribing  this  result 
to  the  mixture  of  the  two  liquids."  The  assumption  of  course 
always  is,  where  a  change  introduced  into  a  given  set  of  cir- 
cumstances is  immediately  followed  by  a  further  change,  that 
without  the  first  change  the  circumstances  would  have  re- 
mained as  they  were,  that  the  second  change  would  not  have 
taken  place.  Thus,  in  the  instance  given,  from  the  chloride 
of  mercury  alone,  without  the  iodide  of  potassium,  no  red 
precipitate  (it  is  assumed)  would  have  been  formed.  The 
iodide  of  potassium  is  accordingly  an  "antecedent  which 
cannot  be  excluded  without  preventing "  the  phenomenon 
observed  :  the  consequent  *  red  precipitate '  can  be  excluded 
with  no  other  difference  in  the  antecedents  than  the  absence 
of  the  iodide  of  potassium.  So  far,  then,  as  we  may  trust  to 
the  Method  of  Difference,  we  reach  the  law  "  Chloride  of 
mercury  added  to  iodide  of  potassium  — >  red  precipitate." 
We  will  not  ask  how  far  these  methods,  and  the  subordi- 
nate variations  of  them,  can  be  trusted  for  proof  of  absolutely 
universal  laws  of  sequence,  whether  of  backward  or  of  for- 
ward reference, — laws,  e.g.,  such  as  "  Wherever  S  is  found, 
5»  must  have  been  before,"  or  "  Wherever  S  happens,  ^  is 
sure  to  follow."     Practically,  as  already  said,  we  are  for  the 

•  Mffl's  Logic,  vol.  i.  p.  450.  (8th  Ed.) 
16 


34)2  APPENDIX. 

most  part  obliged  to  be  content,  in  our  knowledge  of  causal 
sequences,  with  much  less  than  these  completely  universal 
assertions.  The  mass  of  our  propositions  regarding  causal 
laws  are  of  the  milder  type,  "  ^  is  one  cause  of  S,"  or  "  S, 
unless  counteracting  circumstances  interfere,  will  cause  ^  to 
follow." .  It  is  necessary,  therefore,  to  inquire  how  far  the 
empirical  methods  may  be  relied  upon  for  the  support  of 
such  comparatively  timid  assertions  as  these. 

The  Method  of  Agreement. 

Canon. — If  two  or  more  instances  of  the  phenomenon  under 
investigation  have  only  one  circumstance  in  common,  the  circum- 
stance in  which  alone  all  the  instances  agree  is  the  cause  (or  effec() 
of  the  given  'phenomenon. 

It  is  obvious,  in  the  first  place,  where  the  simple  Method 
of  Agreement  fails.  Its  '  characteristic  imperfection,'  as 
Mill  himself  took  care  to  show,  is  due  to  our  necessity  of 
admitting  that  the  *  same  efFect '  may  be  produced  by  *  dif- 
ferent causes.*  Of  course,  as  Mr.  Carveth  Read  puts  it,  an 
effect  particularised  to  the  full  can  never  arise  from  different 
causes ;  but  the  very  essence  of  these  abstract  propositions 
is  that  they  particularise  to  the  full  neither  S  nor  §b,  and  so 
far  as  they  fall  short  of  describing  an  effect  "  in  the  minutest 
detail,"  so  far  they  leave  an  opening  for  vicarious  causes. 
The  manner  in  which  the  vicariousness  ('  Plurality ')  of 
causes  interferes  with  the  cogency  of  the  method  is  easily 
seen.  Assume,  for  instance,  that  I  have  made  ten  observa- 
tions as  to  the  apparent '  effects'  of  eating  salmon ;  having  ten 
times  observed  this  antecedent  to  be  followed  by  indisposi- 
tion. On  each  of  these  occasions  there  have  been  many  other 
circumstances  combined  with  it, — the  other  things  eaten  and 
drunk  during  the  same  period,  to  go  no  further.     In  order  to 


THE  METHOD  OF  AGREEMENT.  343 

put  the  most  favourable  case  possible  for  the  operation  of  the 
method,  we  will  also  suppose  that  the  salmon  was  the  only 
antecedent  common  to  all  the  cases  of  indisposition.  But  if 
vicariousness  of  causes  be  once  admitted  possible,  there  is 
nothing  to  prevent  A  having  been  the  real  cause  on  the  first 
occasion,  B  on  the  second,  C  on  the  third,  and  so  on ;  S  (the 
salmon)  having  been  perfectly  harmless  all  the  while, — just 
as  harmless  as  some  other  circumstance  which,  though  not  part 
of  the  food,  is  invariably  present  in  all  the  cases, — say  the 
fact  that  Bismarck  is  still  alive.  Unless,  in  short,  we  have 
some  further  reason  to  suspect  the  element  in  question  to  be 
the  guilty  one  (in  the  case  supposed,  e.g.,  we  may  rely  on 
popular  belief,  or  doctor's  advice,  or  family  tradition) — un- 
less we  can  bring  deduction  from  some  accepted  truths  to  aid 
us,  the  mere  method  of  agreement  by  itself  can  give,  in  such 
cases  as  these,  no  solid  support  at  all. 

There  is,  however,  it  will  perhaps  be  said,  one  class  of 
cases  in  which  the  unsupported  method  of  agreement  must 
be  allowed  to  be  practically  sufficient;  namely,  where  the 
cases  observed  are  not  counted  by  tens,  but  by  hundreds  or 
thousands  or  more.  But  putting  aside  the  difficulty  of  set- 
tling where  the  sufficient  number  begins,  and  also  the  diffi- 
culty of  finding  an  unmistakable  instance  of  such  a  case, — 
for  where  the  observations  are  numerous  either  the  joint 
method  or  that  of  concomitant  variations  is  usually  appli- 
cable,*— what  is  there  to  prevent  these  thousands  being  all 
under  the  same  limitation  ?  "  We  might,"  as  Mr.  Fowler  says, 
"  pass  through  a  field  containing  thousands  of  blue  hyacinths, 
but  this  would  not  justify  us  in  expecting  that  the  next  time 
we  saw  a  hyacinth  it  would  be  a  blue  one  "  [say  rather,  *  this 

•  Certain  axioms,  e.g.,  sometimes  quoted  in  this  connexion,  seem  to 
me  to  be  more  dependent  on  concomitant  variations  than  on  strict  and 
mere  agreement. 


344  APPENDIX. 

would  nut  prove  that  all  hyacinths  are  blue '].  A  large 
number  of  minor  differences  may  be  thus  eliminated,  and  yet 
some  important  limitation  may  remain  so  as  to  constitute  a 
differentia  common  to  all  the  cases  observed.  In  other  words, 
besides  mere  number  we  need  the  assurance  that  these  in- 
stances are  fairly  representative  of  all  that  exist.  The 
field  of  our  observation  may  be  a  large  one,  but  there  may 
also  be  other  fields  outside  of  it, — until  such  possibility  is 
excluded. 

The  Joint  Method. 

These  difficulties  are  partly  met  by  the  Joint  Method, 
but  not  entirely.  The  Joint  Method  compares  two  sets  of 
instances  independently,  and  combines  the  results.  Its 
canon  is,  in  Mill's  words  : — 

If  two  or  more  instances  in  lohich  the  phenomenon  occurs  have 
only  one  circumstance  in  common,  while  two  or  more  instances  in 
which  it  does  not  occur  have  nothing  in  common  save  the  absence  of 
that  circumstance  ;  the  circumstance  in  which  alone  the  two  sets  of 
instances  differ,  is  the  effect,  or  the  cause,  or  an  indiapensahle  part 
of  the  cause,  of  the  phenomenon. 

The  canon  itself  is  axiomatic,  but  its  application  is  far 
from  being  secure.  To  test  it,  let  us  suppose  the  most  favour- 
able conditions ;  namely,  that  the  instances  observed  are 
considerably  more  than  two  in  number.  Mr.  Fowler  again 
provides  us  with  a  good  example—  "  I  have  observed  that  a 
certain  plant  is  invariably  plentiful  on  a  particular  soil :  if, 
with  a  wide  experience,  I  fail  to  find  it  growing  on  any 
other  soil,  I  feel  confirmed  in  my  belief  that  there  is  in  this 
particular  soil  some  chemical  constituent,  or  some  peculiar 
combination  of  chemical  constituents,  which  is  highly  favour- 
able, if  not  essential,  to  the  growth  of  the  plant." 

It  is  clear  that  if  the  one  set  of  instances  agree  in 


THE  METHOD  OF  DIFFERENCE.  345 

nothing  but  the  presence  of  the  two  circumstances,  and  if 
the  other  set  agree  in  nothing  but  their  absence,  there  is  of 
course  no  room  for  a  vicarious  cause.  But  it  is  just  this 
further  assurance  which  lies  outside  any  possible  apjdication 
of  the  canon,  and  which  must  be  added  to  it  to  complete 
its  cogency  in  a  given  case.  To  refer  to  Mr.  Fowler's  ex- 
ample, we  need  assurance  that  besides  the  chemical  consti- 
tuents of  the  soil  no  other  surroundings  are  invariably  present 
and  absent  together  with  the  soil, — such  as  climatic  condi- 
tions, for  example.  A  wider  experience  may  always,  until 
the  contrary  be  shown,  lead  to  the  necessity  of  qualifying 
(i.e.  limiting)  the  law  arrived  at.  Instead  of  being  simply 
"  This  plant,  in  general,  — >  these  chemical  constituents  in 
the  soil,"  the  law  may  be,  "  This  plant,  under  certain  conditions 
(of  climate  or  otherwise),  — >•  these  chemical  constituents." 
In  its  simpler  form  the  law  remains  liable  to  contradictory 
instances  being  found  on  a  wider  search. 

The  Method  of  Difference. 

Canon. — If  an  instance  in  which  the  phenomenon  under  in- 
vestigation occurs,  and  an  instance  in  which  it  does  not  occur,  have 
every  circumstance  in  common  save  one,  that  one  only  occurring  in  the 
former  ;  the  circumstance  in  which  alone  the  two  instances  differ, 
is  the  effect,  or  the  cause,  or  an  indispensable  part  of  the  cause, 
of  the  phenomenon. 

The  Method  of  Difference  may  be  called  the  sheet-anchor 
of  empirical  proof,  *'  It  .  .  .  appears  to  be  by  the  Method 
of  Difference  alone,"  says  Mill,  "  that  we  can  ever,  in  the 
way  of  direct  experience,  arrive  with  certainty  at  causes." 
Elsewhere  we  frequently  hear  of  its  "  rigorous  cogency." 

An  example  has  been  already  given, — an  example  which 
shows  the  strength  of  the  method  but  not  its  weakness : 


346  APPENDIX. 

when  we  add  iodide  of  potassium  to  chloride  of  mercnry,  we 
may  no  doubt  be  tolerably  sure  of  the  substances  we  are 
handling:  inside  a  test  tube  unknown  antecedents  have  small 
chance  of  entry. 

Granting,  however,  that  this  method  has  a  practical  ad- 
vantage, in  many  cases,  over  the  other  methods ;  and  that 
its  results  are  often  practically  beyond  cavil ;  on  what  does 
its  certainty  depend  ?  Not,  in  any  way,  on  the  method  per  se 
but  on  the  fact  that  in  certain  departments  of  inquiry  (e.</. 
in  chemical  experiments)  we  are  fairly  in  a  position  to  obtain 
the  external  certainty  that  all  the  antecedents  are  known. 
So  far  as  we  can  be  sure  that  we  vary  only  one  circumstance 
at  a  time,  so  far  we  attain  this  external  certainty :  so  far  as 
we  cannot  get  this  assurance  the  method  of  Difference  is  no 
more  safe  than  any  other  suggestive  source  of  inference. 
"Where,  as  in  a  chemical  laboratory,  we  have  practically  entire 
control  over  surrounding  circumstances,  such  as  light,  air, 
and  temperature ;  where  we  can  obtain  any  element,  or  com- 
bination, we  require,  in  the  utmost  possible  purity  and  in 
the  exact  proportion  desired  ;  there  is  no  doubt  this  method 
may  be  trusted  almost  absolutely.  But  the  certainty  is  due 
to  the  laboratory  apparatus  and  not  to  the  method  of  Differ- 
ence by  itself.  "When  we  come  outside  these  highly  artificial 
conditions,  and  attempt  to  apply  the  method  of  Difference  in 
circumstances  over  which  we  have  no  control,  we  find  our- 
selves constantly  brought  up  against  the  fallacy  post  hoc  ergo 
propter  hoc.  To  show  simply  that  in  a  given  case  when  S  was 
added  to  existing  circumstances  Jb  followed,  cannot  prove 
that  S  — >  <S>  unless  we  show  at  the  same  time  that  no 
other  alteration  in  the  existing  circumstances  took  place, — a 
universal  negative  which  in  practice  it  is  often  hard  to  prove 
even  approximately.  In  all  the  more  complex  questions, 
such  as  those  of  politics,  character,  or  daily  life  in  general, 


THE  METHOD  OF  EESIDUES.  347 

firm  proof  by  means  of  the  direct  method  of  Diflference  be- 
comes nearly  impossible.  Witness  the  argument  that  because 
the  addition  of  Free  Trade  to  England's  commercial  system 
has  been  followed  by  periods  of  depressed  activity,  therefore 
the  former  is  the  cause  of  the  latter.  And  the  possibility  of 
conjuring  tricks  is  perhaps  the  clearest  example  that  can  be 
given  of  the  effects  of  unguarded  confidence  in  the  direct 
method  of  Difference.  When  the  conjurer  produces  startling 
effects  by  apparently  insignificant  causes,  there  are  *  un- 
known antecedents'  up  his  sleeve  or  elsewhere  convenient, 
whose  presence  it  has  been  his  business  to  make  us  overlook. 

The  Method  of  Besiduea. 

Canon. — Subduct  from  any  phenomenon  such  part  as  is  known 
by  previous  inductions  to  be  the  effect  of  certain  antecedents,  and 
the  residue  of  the  phenomenon  is  the  effect  of  the  remaining  ante- 
cedents. 

It  is  seldom  that  the  Method  of  Eesidues  can,  or  rather 
need,  be  employed  at  all  as  a  method  of  proof,  though  as  a 
source  of  inference  it  has  often  been  fruitful  and  important. 
Astronomical  discovery  especially  is  full  of  staking  results 
obtained  by  means  of  it :  so,  too,  certain  other  departments 
of  science.  But  of  attempted  proof  by  means  of  Eesidues 
merely,  we  are  rather  hampered  in  finding  true  examples. 
Mill  himself  gives  no  instance  of  its  working,  except  in 
symbols,  and  every  instance  given  by  Professor  Fowler  is 
an  instance  of  discovery,  not  of  proof.  Most  of  those  given 
by  Professor  Bain  are  also  cases  where  suggestive  hints  have 
been  first  given  by  this  method,  to  be  verified  in  other  ways. 

Here  it  is  clear  at  once,  even  without  examples,  that  all 
must  turn  upon  the  exhaustiveness  with  which  the  residue  is 
narrowed  down  by  the  hnown  causes  and  effects  in  the  case. 


348  APPENDIX. 

The  difficulties  of  the  method  of  Difference  are  therefore 
here  repeated,  and  are  further  increased  by  the  fact  that  the 
required  isolation  of  the  phenomena  is  not  actually  attained, 
but  only  seen  by  the  light  of  imagination.  The  negative 
instance  is  obtained  by  deduction,  not  by  direct  experience. 
In  the  last  two  paragraphs  of  Prof.  Bain's  exposition  of  the 
method,  we  obtain  what  seems  to  me  a  valuable  hint  as  to  its 
true  importance  for  purposes  of  proof;  namely,  that  it  may 
be  employed  to  prove  a  negative  result, — to  disprove  some 
supposed  explanation  by  showing  that  the  effects  can  all  be 
accounted  for  in  other  ways.  Thus,  if  it  can  be  shown  that 
the  known  forces  of  inorganic  matter,  operating  in  the  special 
collocations  of  organic  bodies,  will  account  for  the  phenomena 
of  life  without  leaving  a  residuum,  the  theory  of  a  vital 
force,  or  vital  principle,  becomes  unnecessary.  Such  cases  as 
this  are  perhaps  those  for  which  the  method  is  most  adapted  ; 
but  here  too  all  turns  upon  the  "  if  it  can  be  shown."  This 
condition,  and  not  the  mere  fact  of  employing  the  method  at 
all,  is  the  important  matter, 

TJie  Meiliod  of  Concomitant  Variations. 

Canon. — Whatever  phenomenon  varies  in  any  manner  when- 
ever another  phenomenon  varies  in  some  jiarticular  manner,  is 
either  a  cause  or  an  effect  of  that  phenomenon,  or  is  connected  with 
it  through  some  fact  of  causation. 

'  Concomitant  Variations '  is  perhaps  the  most  commonly 
applied  of  all  the  inductive  methods.  Its  application,  ac- 
cording to  Mill,  is  in  proving  "  the  laws  of  those  Permanent 
Causes,  or  indestructible  natural  agents,  which  it  is  impossible 
either  to  exclude  or  to  isolate;  which  we  can  neither  hinder 
from  being  present,  nor  contrive  that  they  shall  be  present 
alone."     And  it  may  be  added  that  in  almost  all  those  vague 


THE  METHOD  OF  CONCOMITANT  VARIATIONS.        349 

and  large  assertions  so  common  in  daily  life,  the  method  of 
Concomitant  Variations  is  continually  employed  in  proof. 
More  than  this,  it  seems  (as  already  said)  not  impossible  that 
certain  Axioms,  such  as  those  of  Geometry,  find  their  best 
support  in  this  method  rather  than  in  the  method  of  Agree- 
ment. The  more  nearly  our  actual  lines  approach  paral- 
lelism, or  our  magnitudes  equality,  the  more  nearly  do  the 
axioms  fit  the  facts  observed :  the  more  one  set  of  antece- 
dent circumstances  resembles  another,  the  more  do  their 
respective  consequents  agree.*  In  certain  cases  such  as  these, 
perhaps,  '  unknown  antecedents '  can  be  shown  to  be  as  im- 
probable as  a  pest  of  mice  to  the  mounted  knight.  But  even 
here  we  are  never  quite  secure  against  their  interference,  and 
what  security  we  have  is,  as  in  all  the  former  cases,  gained 
from  external  sources. 

Good  examples,  usually  given,  of  the  employment  of  this 
method  are  to  be  found  in  the  thermometer  and  the  pen- 
dulum. We  cannot  deprive  a  body  of  all  heat,  and  we 
cannot  entirely  remove  the  Earth  from  the  pendulum, 
nor  the  pendulum  from  the  Earth ;  but  by  observing  the 
variations  we  may  often  obtain  a  law  which  is  practically  as 
secure  as  if  it  were  really  obtained  by  the  direct  method  of 
Difierence.  We  get  abundant  evidence  tending  to  show  that 
if  the  diiect  method  of  Difierence  could  be  applied  (which, 
by  the  hypothesis,  it  cannot),  we  should  have  all  the  cogency 
which  that  method  could  give  us. 

We  should  have  all  that  cogency,  but  no  more.  For  in 
this  case,  as  in  the  case  of  all  the  other  methods,  we  require, 
over  and  above  the  employment  of  the  method  itself,  a  further 
assertion  on  which  its  actual  cogency  in  the  given  case  shall 

*  Cf.  also  the  use  made  by  the  late  Prof.  Jevons  of  his  principle  of 
the  "  Substitution  of  Similars,"  where  "  likeness  or  equivalence "  is 
treated  as  purely  a  matter  of  degree. 


350  APPENDIX. 

depend.  For  Concomitant  Variations,  this  further  assertion 
has  been  expressly  formulated  by  Prof.  Fowler,  as  a  *  rider ' 
to  the  canon : — 

If  we  can  assure  ourselves  that  there  is  no  third  phenomenon 
varying  concurrently  with  these  two,  we  may  affirm  that  the  one 
phenomenon  is  either  a  cause  or  an  effect  of  the  other. 

The  theory  may  in  fact  hold  good  only  up  to  a  certain 
point, — namely,  so  far  as  that  third  phenomenon  (which 
let  us  call  Z)  is  present ;  and  instead  of  S  — >  5),  the  law- 
should  be  accurately  expressed  S  (when  Z  is  present)  — >  S- 
A  well-known  example  of  this  is  the  contraction  of  water  by 
cold,  down  to  39°,  after  which  it  begins  to  expand  again. 
Here  the  limitation  '  above  39° '  must  be  added  to  the  first 
crude  statement  of  the  law  '  water  contracts  with  cold.' 

I  may  add  a  further  difficulty  to  which  the  method  of 
concomitant  variations  is  liable  :  namely,  that  the  supposed 
law  guaranteed  by  it  may  be  a  case  of  varepov  Trporcpov. 
Finding  that  the  size  of  towns  varies  concomitantly  with  the 
size  of  the  rivers  on  which  they  are  built,  an  incautious 
reasoner  might  conceivably  arrive  at  the  law  that  the  size  of 
the  river  was  due  to  the  size  of  the  town.  Hearing  the 
cuckoo  call  its  own  name,  he  might  conceivably  put  this 
down  to  the  cleverness  of  the  bird.  Finding  Hamlet  full  of 
'  quotations '  he  might  suppose  that  Shakespeare  was  sadly 
wanting  in  originality.  Of  course,  these  extreme  cases  are 
mainly  useful  as  affording  food  for  the  comic  papers ;  but 
in  serious  inquiries  such  as  that  of  the  concomitant  varia- 
tions between  new  organic  structures  and  the  need  for  them, 
the  fallacy  is  perhaps  not  quite  unknown.  Or  again,  take 
as  an  example  the  good  old  farmers'  theory  that  '  blight '  was 
either  itself  a  kind  of  disease,  or  at  least  a  sign  of  existing 
disease,  in  plants.  They  pictured  the  plant  'becoming 
diseased,' — m\ich   as  a  man's   digestion   might   get  out  of 


THE  METHODS,  IN  GENERAL.  351 

order;  and,  as  an  effect  of  this,  the  blight  was  supposed  to 
'  come  out,' — much  as  the  man  might  break  out  in  a  rash,  or 
pimples.  But  it  seems  to  be  now  completely  established  that 
the  true  explanation  is  that  blight  is  a  kind  of  fungus,  the 
sports  of  which  take  root  equally  in  the  leaves  of  healthy 
plants  and  unhealthy  ;  but  that,  however  healthy  the  plant 
may  have  been,  the  parasite  drains  its  life,  and  so  causes 
disease, — stunts  the  growth  of  the  plant,  or  taxes  its  fruit- 
bearing  powers,  or  in  some  way  interferes  with  the  normal 
state  of  things.  It  is  thus  often  an  exceedingly  difficult 
matter  to  say  which  of  two  things,  varying  concomitantly,  is 
cause  and  which  is  eflfect ;  and  the  common-sense  view,  based 
perhaps  on  some  loose  analogy,  is  as  likely  as  not  to  reverse 
the  sequence. 

Tlie  Methods,  in  general. 

This,  then,  is  the  difficulty  attending  the  application  of 
all  the  methods, — the  possible  presence,  unsuspected,  of  a 
third  phenomenon  (or  '  unknown  antecedent ')  in  the  cases 
observed  :  so  that  the  real  law,  instead  of  S  — >  5,  should 
be  either  Z  — >  <§,  or  SZ  — >  Sb.  The  first  of  these  two 
alternatives  (namely  that  S  is  purely  accidental  to  <5)  ^^^y 
be  for  practical  purposes  excluded  by  the  Doctrine  of  Chances : 
the  second  alternative  must  remain  in  every  case  possible, 
until  removed  by  special  evidence  outside  and  beyond  the 
mere  fact  of  '  employing  the  method.' 

To  sum  up : — Where  the  Method  of  Agreement  is  employed, 
evidence  should  be  further  produced,  to  show  (1)  either  that 
every  element  but  S  and  ^  has  been  eliminated,  or  (2)  that 
those  remaining  are  accidental  to  Sb ;  and  also  that  the  Plu- 
rality of  Causes  does  not  here  interfere. 

Where  the  Joint  Method  is  employed,  we  require  to  know 


352  APPENDIX. 

further  that  no  other  operative  antecedent  was  present  in 
the  positive  set  of  cases  and  absent  in  the  negative  ones. 

Where  the  Method  of  Difference  is  employed,  we  must  be 
sure  that  only  one  circumstance  has  been  added. 

Where  the  Method  of  Eesidues  is  employed,  we  require 
the  same  external  evidence  as  for  the  Method  of  Agreement. 

Where  the  Method  of  Concomitant  Variations  is  employed, 
we  must  be  further  assured,  (1)  that  nothing  besides  S  varies 
concomitantly  with  ^ ;  and  (2)  that  whichever  (S  or  ^)  is 
supposed  to  be  the  cause  of  the  other,  is  not  in  reality  the 
effect. 

In  each  case  the  real  cogency  of  the  argument  depends 
upon  the  certainty  obtainable  on  these  points :  obtainable  by 
any  external  (and  especially  instrumental)  correction  of  our 
observations,  and  by  searching  analysis  of  the  phenomena 
observed.  The  mere  statement  of  the  method  employed  is 
not  by  itself  a  sufficient  guarantee  :  at  most  it  may  serve  to 
point  out  the  special  direction  in  which  we  should  look  for 
dangers,  and  guard  against  them. 

The  two  main  modes  of  Inductive  fallacy  known  by  the 
time-honoured  names  of  Induclio  per  enumerationem  simplicem, 
and  Post  hoc  ergo  propter  hoc,  correspond  essentially  to  failures 
in  guarding  against  the  dangers  of  the  unaided  methods  of 
Agreement  and  Difference  respectively.  Valid  induction 
often  enough  begins  by  simplex  enumeratio  ;  and  post  hoc  often 
sets  us  on  the  track  of  a  law :  indeed  it  is  difficult  to  suppose 
any  other  beginnings  that  can  be  called  beginnings  of  know- 
ledge. But  it  is  when  the  attempt  is  made  to  Teat  proof  on 
these  alone,  that  the  characteristic  imperfection  of  all  the 
methods  comes  to  be  important.  Unaided  by  special  know- 
ledge of  the  circumstances,  they  are  suggestive  guides  but 
uncertain  testa. 


THE  MOODS  OF  EXCEPTIVE  DISPROOF.  353 

C* 

THE  MOODS  OF  EXCEPTIVE  DISPROOF. 

Before  tracing  in  detail  the  reduction  of  the  fourteen 
syllogistic  moods  in  I  and  0  to  the  two  formulas  given  on 
p.  242  above,|  there  is  a  less  wide  and  general  view  that  may- 
be taken  for  a  moment  with  advantage ;  and  that  is,  the 
view  of  them  as  reducing  a  generalisation  to  absurdity  by 
means  of  the  modes  of  positive  deductive  proof.  In  every 
valid  syllogistic  mood  there  must  be  at  least  one  positive 
indication  among  its  premisses,  and  if  such  premiss  be  com- 
bined with  the  contradictory  of  the  thesis  (i.e.  with  the  posi- 
tive assertion  which  such  Thesis  just  denies)  we  get  as  a  new 
conclusion  either  the  contradictory  or  the  full  contrary  of  the 
other  premiss.  If,  then,  both  premisses  be  in  fact  true,  the 
contradictory  of  the  Thesis  cannot  be  true  :  that  is  the  Thesis 
itself  must  be  so.  Thus  in  the  mood  BaroJco,  the  Thesis  being 
-| — >  <^,  its  contradictory  is  S  — >  <§  :  combine  this  with 
the  positive  premiss  ^  — >  M,  and  (by  Barbara)  we  get  the 
conclusion  S  — >  M.  But  this  contradicts  the  remaining  pre- 
miss of  BaroJco,  namely  S  -j — ^  M,  and  accordingly  one  of  the 
premisses  in  our  Barbara  must  be  materially  false.  But  the 
premiss  5fe  — >  M  is  given  true :  thus  the  fault  is  shown  to 
lie  in  the  remaining  premiss  S  — >  ^ :  and  this  being  false, 
our  Thesis  is  necessarily  true.  It  is  needless  to  set  out  all  the 
forms,  but  if  the  reader  cares  to  trace  the  process  in  them,  he 
will  find  that  BoJcardo  also  employs  Barbara:  that  Festino 
and  Disamis  employ  Celarent :  Ferio  employs  Cesare :  Darii, 
Felapton,  and  Ferison  employ  Cameatres ;  while  the  four 
moods  belonging  to  the  fourth  figure  employ  Camenes. 

*  See  p.  241. 

t  And  see  formulo9  (1)  and  (11)  on  p.  355. 


354!  APPENDIX. 

In  practice,  however,  any  method  based  on  this  view  of 
the  argument  from  exception  would,  I  think,  be  ftmnd 
intricate  and  unwieldy.  The  only  purpose  of  mentioning 
it  is  in  order  to  admit  that  on  occasion  the  arguments  from 
sign  and  from  essential  diflference  (and  even  the  almost  non- 
existent form  Gamenes)  may  be  thus  utilised  in  Disproof  by 
exception.  But  since  all  are  also  translatable  into  one 
or  other  of  the  two  forms  above  given,  which  two  are  in 
a  sense  typical  and  fundamental ;  and  since,  in  fact,  the 
amount  of  translation  necessary  in  order  to  bring  them 
under  the  appropriate  formula  is  of  the  easiest  possible 
description,  it  seems  better  worth  while  to  follow  the 
inquiry  in  this  direction. 

If  we  take  the  fourteen  syllogistic  moods  whose  conclu- 
sions are  in  I  and  0,  it  will  be  seen  that  these  two  formulas 
are  generalised  from  them,  by  omission  of  the  distinctions  of 
quality  in  M  and  5  respectively,  by  free  employment  of  the 
law  of  counter-indication,  and  by  confining  attention  to 
the  smallest  amount  of  assertion  necessary.  There  is  only 
one,  for  example,  which  exactly  corresponds  with  our  first 
formula,  namely  BaroJco,  and  only  one  which  exactly  corre- 
sponds with  our  second,  namely  Bokardo.  All  the  others 
may  be  viewed  as  varieties  of  these  two. 

Thus,  in  the  first  place,  with  M  negative  instead  of 
positive,  we  get  Festino ;  with  M  and  <§  both  negative  and 
with  the  counter-equivalent  of  the  required  non-<^  — >  non-M 
(namely  M  — >  ^)  we  get  Darii.  Witli  these  differences 
and  also  with  the  counter-equivalent  of  the  required  S  -| — > 
non-M  (namely  M  -| — >  non-S)  we  get  Datisi ;  and  if  instead 
of  merely  M  -\ — >  non-S  in  this  latter  mood  we  can  make 
the  positive  assertion  M  — >  S,  we  get  Darapti.  With  M  nega- 
tive and  with  the  counter-equivalent  of  the  required  ^  — > 
non-M  (namely  M  — >  non-<^)  we  get  Ferio  ;  with  the  same 


THE  MOODS  OF  EXCEPTIVE  DISPROOF. 


355 


differences  and  also  the  counter-equivalent  of  the  required 
S  -i — >  non-M  (namely  M  -\ — >  non-S)  we  get  Ferison  ;  and 
if  here  we  can  make  the  positive  assertion  M  — >  S,  we  get 
Felapton.  Finally,  with  M  negative,  and  only  the  minor 
premiss  reversed  (namely  M  -\ — >  non-S  instead  of  S  -\ — > 
non-M)  we  get  Fresison ;  and  if  this  be  strengthened  into 
M  — >  S,  we  get  Fesapo. 

Similarly,  in  the  second  class,  with  5  negative  we  get 
Disamis :  with  the  same  difference  and  also  with  the  counter- 
equivalent  of  the  required  M  -\ — >  non-^  (namely  <£  H — > 
non-M  we  get  Dimaris  ;  and  if  this  be  strengthened  into  the 
positive  assertion  ^  — >  M,  we  get  Bramantip. 

A  table  may  be  of  service  to  the  reader  in  verifying 
these  details  :-^ 


(1) 

Baroko   . 

S-j->a>         forS-l->M        andS->M 

(2) 

Festino    . 

Ditto                 „    S  -f^  non-M    „  &  — ^  non-M 

(3)       Darii      , 

S  -|->  non-a    „    S  -}->  non-M    „  M  ->  & 

(4")  1    Datisi     . 

Ditto                 „    M  +>  non-S    „  M  — ^  => 

(5)       Darapti . 

Ditto                 „    M  — >  S           „  M  — >  S> 

First 

(6) 

Fiiio 

S  -f^  S          „   S  4-^  non-M    „  M  — >  non-S 

formula. 

m 

Ferison  . 

Ditto                „   M  -f->  non-S    „  M  — ^  non-S 

(8)       Felapton 

Ditto                 „    M  — >  S            „  M  — >•  non-S 

[9)       Fresison 

Ditto                 „    M  -[->  non-S    „  S  — ^  non-M 

(10) 

Fesapo    . 

Ditto                 „    M  — ^  S           „  S  — >  non-M 

(11)  1    Bokardo. 

Ditto             „   nr  -^  S         „  M  -!->  s 

(12) 

Disamis  . 

S  -j->  non-S  »    M  — >  S           „  M  -H>  non-S 

Second 

(13)      Dimarit 

Ditto                „    M  — >  S           „  S  4->  non-M 

formula. 

(14) 

Bramantip 

Ditto                ,.    M->S           „S— >M 

It  will  be  seen  that  the  syllogistic  moods  corresponding 


356  APPENDIX. 

to  our  first  formula  are  nearly  three  times  as  numerous  as 
those  corresponding  to  the  second  ;  but  the  second  is  not  on 
this  account  at  all  less  important,  or  even  less  frequently 
met  with  in  practice.  All  the  syllogistic  moods  are  possible, 
indeed,  but  some  are  no  more  than  possible,  and  certainly 
not  all  these  fourteen  forms  are  equally  employed.  Probably 
the  seven  commonest  are  Baroho,  Festino,  Darii,  Ferison,  Datisi, 
JBoTcardo,  and  Disamis.  Of  these  the  six  last  form  three 
pairs,  differing  only  in  the  quality  of  5;  the  reason  that 
*  BaroJco  has  no  kindred  form  in  I  is  that  for  such  form  the 
disjunctive  non-5  — >  M  would  have  been  required,  and 
the  disjunctive  had  no  place  amongst  the  moods  of  the 
scholastic  scheme. 


D.* 

INVARIABLE  SUCCESSIOIT. 

In  accordance  with  the  plan  proposed  in  this  book,  I  have 
tried  to  keep  away  from  all  the  deeper  problems  in  the 
theory  of  causation.  This  was  partly  on  account  of  their 
difficulty,  but  also  because,  whatever  other  elements  may  be 
involved  in  the  notion  of  causal  sequence,  the  element  of 
invariability  appears  strictly  sufficient  for  the  purposes  here 
aimed  at. 

The  '  cause '  of  a  thing  comes  now  more  and  more 
to  mean  its  '  history.*  The  assumptions  seem  more  and  more 
justified,  that  if  past  events  had  been  at  all  different  this 
present  event  or  thing  would  not  have  been  precisely  what 
it  is ;  that  if  they  had  been  '  essentially '  different  this 
would  have  been  essentially  different  also ;  and  hence,  that 
if  the  essential  part  of  this  event  be  fixed  by  definition,  to 
*  See  p.  81. 


INVARIABLE  SUCCESSION.  357 

Buch  essential  part  there  corresponds  a  part  of  the  antecedent 
history,  which  not  happening  the  event  in  question  (happen- 
ing there  and  then)  would  have  been  too  diflferent  to  deserve 
its  present  name. 

But,  as  noticed  elsewhere,  the  fixing  of  a  definition  is 
never  "particularisation  to  the  full."  Hence,  within  the 
limits  allowed  by  the  name,  there  is  room  also  for  difference 
in  the  antecedent  circumstances  (i.e.  for  Plurality  of  causes), 
and  therefore  we  are  led  to  read  the  essentiality  only  from 
effect  to  cause  (the  indication  from  cause  to  effect),  and  to 
use  the  concept  '  invariable  law '  in  preference  to  that  of  the 
*  identity '  of  cause  and  effect. 

In  all  cases  of  '  invariable '  sequence  in  which  S  and  <^ 
are  not  regarded  directly  as  cause  and  effect,  the  assertion  of 
invariability  is  either  expressly  stated  as  conditional,  or 
intended  as  tentative  (or  '  empirical ')  only.  In  the  often- 
quoted  case  of  day  and  night,  for  example,  experience  tells 
us  not  only  that  day  always  follows  night,  but  also  that  night 
follows  day,  and,  further,  that  day  alwa3S  follows  sunrise  and 
night  sunset.  We  thus  get  a  double  observation  (under  the 
joint-method)  in  favour  of  the  commonly  received  explana- 
tion of  the  phenomena,  while  the  supposed  assertion,  '  night 
causes  day,'  could  only  rest  upon  the  method  of  agreement, 
and,  even  in  the  absence  of  the  other  explanation,  would  be 
of  very  uncertain  tenure, — being  np  explanation  of  more 
than  half  the  facts  observed.  It  would  be  an  empirical  law, 
entirely  unconnected  either  with  wider  laws  which  might 
explain  it,  or  with  other  facts  which  itself  might  explain ; 
and  it  would  also  be  open  to  the  obvious  criticism  that 
nothing  had  been  shown  to  prove  that  the  dependence  was 
not  exactly  the  reverse  way, — day  causing  night,  as  daily 
exertion  (it  might  be  suggested  by  the  poetic  mind)  causes 
nightly  sleep. 


358  APPENDIX. 

Invariability  of  succession  is  then  what,  in  assertions  of 
causation,  we  always  do  mean  to  express,  whether  we  also 
include  TJnconditionality  (or  Efficacy),  or  keep  our  assertion 
close  to  the  facts  from  which  these  highly  abstract  notions 
take  their  rise.  The  sequence  of  night  and  day,  viewed 
merely  as  sequence,  and  apart  from  all  question  of  efficacy, 
is  not  contradicted  by  the  establishment  of  the  surer  sequence 
"  Earth's  revolution  in  sunlight  — >  day  and  night  alter- 
nately," but  is  merely  merged  in  this,  and  loses  thereby 
whatever  independent  value  it  might  otherwise  have  had  as 
an  engine  of  explanation  and  prediction.  So  far  as  it  is  for 
these  two  purposes  only  that  we  need,  or  use,  the  notion  of 
Causation,  Invariability  is  sufficient. 

Nor,  on  the  other  hand,  if  we  picture  causes  as  liable  to 
'  counteraction,'  need  the  absence  of  actual  invariability 
present  a  stumbling  block.  Although,  for  example,  the 
majority  of  seeds  never  actually  come  to  anything,  our 
knowledge  of  the  causes  of  failure  permits  us  to  infer  that 
but  for  certain  obstacles  that  may  be  classed  and  numbered, 
they  would  do  so.  So  far  only  as  the  definite  possibilities  of 
counteraction  remain  unknown,  so  far  we  admit  an  element 
of  uncertainty  in  any  predictions  based  on  our  causal  law. 
In  such  a  case  the  statement  of  the  law  itself  is  felt  to  need 
some  further  limitation. 


APPENDIX. 


359 


E. 

TABLE  I  • 

Abstract  and  Concrete,  Affirmation  and  Denial. 

[— ^  being  the  symbol  of  indication ;  -|->  for  exceptive  and  simple 
denial  of  indication  ;  and  ,~^  for  the  assertion  of  difierence.j 

Propositions. 


UnreaL 


Bed. 


Abstract. 


Concrete. 


Assertive 
(or  affirmative). 

s->s.. 

(e.gr.    'Children 

never  think  of 

others.') 


Denial. 


Exceptive 

{e.g.  '  Some 
children  are 
nnselflsh.') 


Assertion  of 
difference. 

(e.g.  'Whales 
are  not 
fishes.') 


Assertive 

(or  affirmative). 

This  S  — >  a.. 

(?.gr.  '  This  »  as  due 

to  carelessness.') 


Denial. 


Simple. 

This  S  +>  S. 

(e.g.  'This  was 

not  due  to 
carelessness.') 


Assertion  of 

difference. 

This  S , — ^  a.. 

(e.(/.  'This 
case  differs 
from  that.') 


•  See  pp.  41-79. 


3G0 


APPENDIX. 


TABLE  II.* 

Succession  and  Co-existenciii. 
Eeai,  Pbopositions. 

(Whether  abstract  or  concrete,  assertive  or  negative :  the  symbol 
being  used  to  generalise  — >■  and  -f^.) 


Of  succe'ssion. 


Of  co-existence. 


Explanatory 
and  detective. 


'  past  &. 

'  Valleys  are  due  to 

denudation.' 
'  Tliis  mark  was  caused 

by  ice.' 


Predictive. 


■  future  S. 


'  Deficient  education 
favours  crime.' 

'  Tliis  law  will  not 
pacify  Ireland.' 


Descriptive, 

classifying, 

and  connecting. 


S  -j-^  present  S. 
S  ' —  present  S, 

'Gold  Is  aa  elementary  sub- 
stance.' 

•Business  qualities  and  the  san- 
guine temperament  generally 
go  together.' 

'  This  man  is  guilty.' 

'  Whales  are  not  fishes.' 

•  This  case  differs  from  that.' 


[This  table  intentionally  leaves  out  of  consideration  the  further  dis- 
tinctions due  to  '  laws  only  roughly  true  : '  for  these,  see  Table  III.] 


See  pp.  19-S3. 


APPENDIX. 


361 


TABLE  III.» 

The  Questions,  eegakding  Indication,  to  one  of  which  eveey 
Thesis  gives  the  answer  Yes  or  No. 


DoesS— ^S?— 
(S  being  given, 
and  &  doubt- 
ful, except 
in  the  case 
marked  *). 


8  being  spoken 
-    of  in  the  ab-  — 
Btract. 


&  in  the  past  re- 
—     latively  to  S. 


/The  asserted  in- 
dication being 
strictly  inter- 
preted. 

I  With  unex- 
pressed quali- 
fication. 


(Is  S  neces- 
sary to  S  as 
cause?) 


■)  (Is  S  on< 
V     ofS?) 


/Strictly. 


S  in  the  present  - 
"     relatively  to  S, 


With        unex- 
pressed quail' 
.    lication. 


'■•} 


S  in  the  future 
"    relatively  to  S. 


(Does  Si  always 
co-exist  with 
Sf) 

(Does  S  usually 
co-exist  with 
S?) 

(Is  S  the  in- 
evitable effect 
of  S  ?) 


With        unex-  "|  (Does  S  tend  to 
pressed  quali-  j-    produce  &  ?) 
fication. 


/Strictly. 


s-)( 


S  being  spoken 
of  in  the  con-  ' 
Crete  (i.e.  as 
-  particularised 
by  its  indivi- 
dual peculi- 
arities and 
cnvironmeut). 


...*  (Was  the  actual  sequence  or  co-existence,  S  followed 
or  accompanied  by  S,  other  than  accidental  ?) 

-^  Mi*veVto  s'"  }  CI>'d  S  happen,  causing  S  ?) 
-*^al!^l5fS}(^V»lS^"-S0 


See  pp.  41-83. 


362 


APPENDIX. 


TABLE  IV.» 

The  Types  of  Augvment. 

Argtiments. 


By  Example. 

1 

By  Sign. 

Analogy. 
(S  — Z 

Proof  of  Law 
from  Fact. 

(M->Z 

for 
here  are  cases 
of  which  this 
law  is  the  best 
explanation.) 

Proof 
by  Sign. 

for 
•See  pp. 

1                              1 
Distinction  by           Exceptive 
Point  of                  Dispioof. 
Difference.                       1 
(S~S.:                          1 

for 

lor                      1                       1 
S— >-M         By  Sign  or      By  Example 
S— >iion-M.)   Difference. 

(S+>&:        (S+^&: 
for                     for 

Sb-^U.)        M-5.S.) 

224-238. 

APPENDIX. 


363 


TABLE  v.* 

TflE  Dangers  Peculiar  to  the  Special  Types  op  Argument. 
In  the  Argument : — 


By  Example. 

(Danger :  unsuspected  and  essentiaX 
difference.) 


By  Sign. 

(Danger :  acceptance  of  a  Principle 
which  does  not  apply. 


(1)  Analopy.  (2)  Generalisation. 

(Danger :    essen-  (Danger :    essen- 

tial difference  be-  tial  difference  be- 

tween S  and  SO  tween  This  S  and 

All  S.) 


I 

(3)  Ignorance  that 
Principle  and 
Application  are 
needed:  or  what 
ttiey  should  be. 


(4)  Acceptance  of  the 
reciprocal  of 
either  Principle 
or  Application  as 
equivalent. 


Unsuspected  difference 
or  resemblance  be- 
tween the  '  things ' 
spoken  of,  through 
the  influence  of 
names. 


(6)  Difference  between 
things  named 
alike. 


(6)  Resemblance  be- 
tween things 
named  differ- 
tmtly. 


Bee  pp.  252-297. 


INDEX. 


Absence,  indication  by,  84,  92 ;  and 
presence,  specially  defined,  85. 

Abstraction,  in  general,  72,  333  ; 
abstract  propositions,  66,  76,  78, 
80,  112,  235,  272,  276,  339 ;  ab- 
stract terms,  72. 

Absurdity,  reduction  to,  298,  174, 
251,  286,  307,  326,  328. 

Accident.     See  Essence. 

Acddentis  Fallacia,  293,  176. 

Adequacy  of  Keason  given.  111, 
102,  300,  26. 

Admissions,  appeal  to,  114,  181 
note,  207. 

AfBrmation  and  Denial,  64,  68, 
223,  243. 

Agreement,  Method  of,  342,  281, 
339,  351 ;  as  to  meaning,  neces- 
sity of,  16,  57,  65,  145,  183. 

Alternative  theories,  need  for  con- 
sidering, 39,  40,  164,  177,  270, 
275,  276,  310,  311,  328;  list  of, 
333. 

Ambiguitv,  verbal,  124,  133,  177, 
184,  189. 

Analogy,  as  argument,  226,  252, 
179,  212,  214;  and  metaphor, 
198  note,  259 ;  and  essential  re- 
semblance, 227,  247,  267;  and 
deduction,  229  note,  231,  232, 
234,  254 ;  dangers  of,  252 ;  vital 
point  of,  267;  usual  modes  of 
employing,  262 ;  analogical  con. 
sisteucy,  110,  104. 

17 


Analysis,  value  of,  258,  237,  273, 
279,  317 ;  and  synthesis,  259. 

Analytical  proposition,  42  note. 

Antecedent  and  Consequent,  222, 
290. 

Antecedents,  unknown,  danger  of, 
270,  279,  284,  349,  351. 

Application,  of  Principle,  111,  113, 
103,  109,  204,  208;  remote  and 
direct,  303,  308,  210. 

Argument,  real  and  verbal,  204; 
special  types  of,  202 ;  as  com- 
plex proposition,  100,  58,  64, 
310  ;  and  rules  for  debate,  160, 
163 ;  by  example,  224,  220,  252 ; 
by  sign,  239,  286,  220;  hypo- 
thetical and  categorical,  221 ; 
ad  hominem,  61,  181  note,  205 ; 
by  analogy,  226,  252,  179,  212, 
214;  inductive,  234,  267;  de- 
ductive, 242,  286;  chain,  210, 
303,  308;  obstruction  of,  50, 
128,  167 ;  a  list  of  objections  to, 
178. 

Aristotle,  174,  176,  179,  193,  209, 
293. 

Assertion,  in  general,  41 ;  and 
denial,  64,  68,  223;  and  con- 
clusion, 33,  18,  41,  150 ;  unsup- 
ported, 147,  326;  of  difference, 
68,  246 ;  of  donbt,  153  ;  implied 
by  Thesis  and  Reason,  99,  26, 
27, 114,  288,  300  ;.goal  and  start- 
ing-point of,  54 ;  degrees  of 
reality  in,  146 ;  suggestive  and 
tentative,  151,    227,   252,    259, 


866 


INDEX. 


162, 188 ;  vagnenesB  of,  49,  187, 
251;   and  meaning,  26,  60,  63, 

183.  See  also  Proposition. 
Associations,  gathered,  in  names, 

184,  191,  199. 
Assumptions,  covert  and  open,  180, 

181  note,  194,  198  note;  neces- 
sary for  language,  13,  46,  106, 
134;  for  explanation  and  pre- 
diction, 13,  272,  302. 

Attack,  successful  resistance  to, 
37,  38,  249,  273. 

Axiom,  and  nndeniability,  285 ; 
and  theory,  207,  285 ;  and  plati- 
tude, 80;  proof  of,  343  note, 
349  ;  of  Syllogism,  301  ;  of 
Causation,  272,  302. 

Axioms,  of  Consistency,  105,  14, 
21,  46,  122,  208;  for  the  indue- 
tive  methods,  340. 


B. 

Bain,  Professor,  56,  87,  89,  105, 
125,  134,  142,  222,  274,  347, 
348. 

Belief,  reasons  and  causes  of,  33 ; 
rationalisation  of.  111,  213  ; 
difficulties  of  grounding,  33,  46, 
48,  149,  309 ;  repression  of,  by 
Logic,  20,  314,  326 ;  in  Mystery, 
48,  14D,  315;  unbelief  and  dis- 
belief, 153,  326 ;  provisional,  94, 
164;  and  opinion,  162,  151,  98, 
325 ;  fluctuation  between  con- 
tradictory beliefs,  120,  140. 

Bentham,  George,  190. 

Bentham,  Jeremy,  198. 

Berkeley,  72. 

Bulls,  129. 

Burden  of  Proof,  148,  247,  277, 
310,  325. 

a 

Casnistiy,  132,  253. 
Categorical  proposition,  73;  argu- 
ment, 221. 


Causation,  metaphysicB  of,  14; 
axiom  of,  272,  302 ;  propositions 
asserting,  54,  79;  and  indica- 
tion, 79,  82,  268,  356  ;  and 
counteraction,  80,  270,  342,  358; 
and  uniformity  of  nature,  272, 
302,  356 ;  causal  dependence, 
63 ;  and  efficacy,  358 ;  kinds  of 
cause,  334,  269  ;  identity  of 
cause  and  effect,  357;  vera  causa, 
238,347,348;  plurality  of  causes, 
80,  270,  342,  351;  ancestral 
cause  of  coexistent  events,  336, 
278  note;  cause  and  history, 
356. 

Chain  arguments,  210,  303,  308. 

Chance,  tendency,  and  law,  81, 
268;  elimination  of,  274,  351, 
270;  necessity  of  recognising, 
337,  81. 

Circle,  120,  169,  213.  See  cdao 
Petitio  Principii. 

Circular  definition,  123,  142. 

Circumstances,  essential,  272,  340; 
control  of,  281,  346  ;  exact  simi- 
larity impossible,  272;  circum- 
stantial evidence,  221,  224. 

Classification,  63,  64,  171 ;  and  see 
Names;  of  fallacies,  170,  171, 
176  ;  classifying  propositions, 
53,  54,  79,  83. 

Co-effects,  335. 

Co-existence,  64 ;  and  succession, 
78,  46,  278  note,  281,  325,  337 ; 
incomplete  indication  of,  82 ; 
and  ancestral  cause,  336. 

Coincidence.     See  Chance. 

Common  sense,  untrustworthiness 
of,  2,  4,  5,  77,  98,  160.  169,  317, 
321,  323. 

Compartmental  view  of  proposi- 
tions, 53. 

Complex  proposition,  only  gradu. 
ally  distinct  from  simple,  56 ; 
argument  as,  58,  64,  100,  310. 

Conclusion,  33,  41 ;  and  thesis,  18, 
150. 

Conclusive  proof,  40, 114, 157,  204, 
220,  275,  285,  300,  329. 


INDEX. 


SG7 


Concomitant  Variations,  method 
of,  348,  339,  343,  352. 

Concrete.     See  Abstraction, 

Confusion,  fallacies  of,  170,  173, 
177. 

Congruent  facta,  as  Proof,  219, 
224,  215,  279. 

Connotation,  53  note,  107.  See 
also  Meaning. 

Consistency,  103,  109,  114,  207, 
317,  328;  Axioms,  Maxims,  or 
Postulates  of,  105,  14,  21,  46, 
122,  208;  deductive  and  analo- 
gical, 110,  103,  104. 

Continuity  of  Nature,  336,  133, 
14. 

Contradiction,  law  of,  105,  106, 
109,  328. 

Contradictory  instance,  250,  271, 
275,  283. 

Contraposition,  84,  87. 

Conversion,  84,  87. 

Copula,  54. 

Counteraction,  of  law,  82,  270, 342, 
358. 

Counter-indication,  law  of,  84;  and 
contraposition,  84  note,  87;  gives 
the  sole  equivalent  form,  86, 
208;  table  of,  87;  use  of,  84, 
89,  310,  329 ;  value  chiefly  nega- 
tive, 90;  and  the  disjunctive 
proposition,  92;  applied  to  con- 
Crete  propositions,  95 ;  as  re- 
gards past  and  future,  96. 

Criticism,  value  of  hostile,  33,  39, 
60,  204,  232,  301,  315. 

Crucial  instance,  235  note. 


Deduction,  110  note,  330;  and 
Syllogism,  113,  212,  300;  and 
Induction,  212,  177,  330,  204; 
and  Proof,  213,  217 ;  and  Petitio 
principii,  194;  and  Analogy,  231, 
229,  234,  254;  and  Inference, 
216}  principle  required  for,  213, 


245,  287,  288,  290;  deductive 
consistency,  110,  108;  deductive 
argument,  kinds  of,  242;  dangers 
of,  286,  287. 

Definition,  consists  in  exclusion, 
39,  93  ;  limits  of,  140 ;  per  genvs 
et  differentiam,  108 ;  ordinary, 
best,  and  special,  125,  127, 137 ; 
as  remedy  for  unreal  assertion, 
119,  127,  134;  difficulties  of, 
124,  127,  133;  circular,  123, 
142;  ignotum  per  ignotius,  142; 
definitions  as  postulates,  122. 

Demonstration,  as  an  ideal,  301, 
195,  232;  how  far  conclusive, 
205;  and  Eeal  proof,  203;  im- 
mediate  and  mediate,  95,  208; 
demonstrative  arguments  rare, 
209. 

De  Morgan,  92,  93,  130,  150,  159, 
180,  193,  194,  251. 

Denial,  64,  68,  223,  243  j  exceptive, 

68,  249. 
Denotation,  107. 
Dependence,  63,  74. 
Descriptive  proposition,  54,  83. 
Dictum  de  Omni,  301. 
Difference,  108,  135,  255,  281,  294, 

302,  330,  344 ;  power  of  seeing, 
256,  193,  330;  essential,  247, 
248,  356;  indistinct,  246;  as- 
sertion of,  68,  246 ;    points  of, 

69,  228,  246;  neglect  of,  108, 
254,  256,  270,  293 ;  method  of, 
345,  277,  281,  339,  352 ;  distinc- 
tion by  point  of,  246,  241. 

Dilution  of  Fallacy,  130, 196. 

Disbelief  and  unbelief,  326, 154. 

Discovery.     See  Inference. 

Disjunctive  proposition,  special 
danger  of,  92. 

Disproof,  and  absence  of  proof, 
151,  165 ;  as  means  to  proof, 
113;  exceptive,  249,  353,  241, 
242;  frustration  of,  149,  310; 
use  of  syllogistic  moods  in,  243, 
248 ;  easier  than  proof,  250,  275, 
279 ;  under  Method  of  Eesidues^ 
348. 


368 


INDEX. 


Distinction  by  point  of  difference, 

246,  241. 
Division,  line  of,  133,  39,  93,  106, 

124, 
Doubt,  assertion  of,  153. 


E. 

EflBcacy  in  causation,  358. 
Elements  of  an  event,   237,   272, 

340,  348.     See  also  Analysis. 
Elimination  of  Accident,  274,  351, 

270,  340. 

Ellipsis  in  expression,  189,  210, 
260. 

Empirical  law,  285,  286,  357; 
proof,  234,  19,  204,  212,  215, 
217;  methods,  277,  339. 

Enumeratio  simplex,  270,  352. 

Epigram,  45,  129,  132. 

Error,  reduction  to  minimum,  117; 
psychology  of,  14,  22. 

Essence,  and  accident,  83,  293, 
335,  336  note,  338;  essential 
resemblance,  229,  64,  253,  254 ; 
ditto  asserted  in  every  analogical 
argument,  266 ;  essential  dif- 
ference, 247,  248,  356 ;  essential 
elements  of  an  event,  237,  272, 
340,  348;  essential  and  acci- 
dental propositions,  42,  125. 

Establishment  by  testing,  37,  39, 
249. 

Etymology,  nse  and  abuse  of,  37, 
105,  190. 

Events,  as  abstractions,  333 ;  ana- 
lysis of,  237,  272,  340,  348. 

Evidence,  21,  148;  varies  in 
strength,  40,  308,  311,  328; 
relevancy  of,  101,  111,  182; 
hearsay,  148,  221 ;  circumstan- 
tial, 221,  224;  aid  of  special 
knowledge  in  judging,  22,  25, 
26,  310. 

Example,  argument  by,  224,  220, 
252. 

Exception,  and  rule,  36,  249,  273, 

271,  279. 


Exceptive  denial,  68 ;  disproof, 
249,  353,  241,  242. 

Excluded  Middle,  law  of,  185, 105, 
106. 

Exclusion  and  definition,  39,  93. 

Experimental  (inductive,  or  empi- 
rical) Methods,  general  discus- 
sion of,  277 ;  in  detail,  339 ;  as 
means  of  discovering  exceptions, 
274;  as  shifting  burden  of  proof, 
277;  as  ideals,  282,  310;  re- 
ducible to  two,  281,  339;  nn- 
satisfactoriness  of,  282,  339 ; 
fundamental  resemblance  of  all, 
282 ;  further  evidence  required 
in,  279,  351 ;  experiment,  pre- 
cautions in,  277,  309,  352. 

Explanation,  the  coimterpart  of 
Proof,  111;  assumptions  required 
for,  13,  272,  302 ;  and  reduction 
to  law,  74 ;  limits  of,  128,  142  ; 
the  'best,'  250,  271,  272;  ex- 
planatory propositions,  83,  123, 
219. 


P. 


Fact,  and  law,  66,  61,  224,  219, 
215 ;  and  theory,  161,  207  225, 
279,  76,  157,  213,  306;  con- 
gruent, 219,  224,  215,  279. 

Factor  overlooked,  201,  181,  252, 
278. 

Fair  presumptions,  158,  94. 

Faith  and  hesitation,  162,  285, 
314,  331. 

Fallacy, ^nd  Sophism,  9;  study  of, 
8,  22;  real  and  verbal,  214,  204; 
avoidance,  detection,  and  con- 
viction of,  22,  23,  31,  118,  200, 
287,  291,  298;  classification  of, 
170,  171,  176;  dilution  of,  130, 
196;  various  senses  of,  172; 
may  be  due  to  several  causes, 
170,  289. 

Fluctuation  of  belief,  120,  140. 

Formal  adequacy  of  Reason,  26, 
111,  102,  300. 


INDEX. 


369 


Fowler,  Professor,  237,  340,  341, 
343,  344,  347,  350. 

Further  assertion  implied  by  The- 
sis and  Reason,  26,  27,  99,  114, 
288,  300. 

6. 

Gaps  in  reasoning,  114,  210,  310, 

311,  326. 
Generalisation,    and    abstraction, 

72,  333;  attack  on,  279;  rests 
on  neglect  of  difference,  254, 
272;  and  exception,  273,  279; 
implied  in  concrete  proposition, 
76;  danger  of,  270,  256.  See 
also  Law. 

General  Names,  use  of,  107,  190; 

and  symbols,  96;  and  definition, 

124,  133,  141. 
Genus,  and  Differentia,   108,   135, 

255,   281,    294,  302,    329,  344; 

summum,  141. 
Grammar,  and  Logic,  15,  57,  65, 

73,  183,221,  223;  and  Language, 
4,  64,  66,  69,  73,  97,  183. 

Goal  of  an  assertion,  54. 
Guesswork,  employment  of,  in  de- 
tecting Fallacy,  169,  218. 
Guidance  of  reasoning,  17. 


Hamilton,  Sir  W.,  18,  42. 

Hearsay  evidence,  148,  221. 

Hesitation,  162,  285,  258,  314,  331. 

Hypothesis,  164,  215,  271,  283, 
285  ;  hypothetical  proposition, 
67,  73  J  hypothetical  argument, 
221. 


I. 


Identity,  law  of,  105,  106,  109, 
122 ;  of  cause  and  effect,  357 ; 
identical  propositions,  42. 

Ignorance,  profession  of,  154,  156. 


Ignoratio  elenchi,  182,  121,  150 
note,  177,  178,  197 ;  finer  shades 
of,  189. 

Ignotum  per  ignotiiis,  142. 

Illicit  process,  173,  223. 

Illusion,  181,  207,  322. 

Immediacy  of  sequence,  281. 

Immediate  inference,  95,  208. 

Implication,  and  Logic,  21,  25, 
107;  and  Indication,  60.  See 
also  Meaning,  and  Consistency. 

Import  of  propositions,  four  views 
of,  53. 

Imposaibile,  diictio  per,  174  note, 
353. 

Inconceivability  of  opposite,  285. 

Inconsistency.  See  Self-contradic- 
tion. 

Indication,  the  most  general  rela- 
tion, 59 ;  and  sign,  79,  107,  113, 
239,  245,  301 ;  and  names,  107 ; 
contrasted  with  implication,  60 ; 
chief  difficulty  of  the  name,  61; 
abstract  and  concrete,  61,  62; 
incomplete,  80,  268;  law  of 
counter,  84;  in  concrete  propo- 
sition, 61;  in  induction,  214, 
309 ;  time-element  in,  96 ;  of 
Thesis  by  Reason,  99,  204,  211, 
244,  310,  329 ;  and  causation, 
79,  82,  268,  356;  and  meaning, 
60,  63,  107. 

Indistinct  difference,  246;  resem- 
blance, 226. 

Individuality,  and  differentia,  254. 

Induction,  and  Logic,  276,  330; 
and  neglect  of  difference,  270; 
contrasted  with  deduction,  212, 
177,  204,  330;  dangers  of;  267, 
270 ;  and  incompleteness  of 
Principle,  214,  308,  309 ;  induc- 
tive inference  and  proof,  215, 
234,  272;  inductive  methods, 
277,  339 ;  and  unknown  antece- 
dents, 270,  279,  284,  349,  351. 

Inference,  ambiguities  of  the  name, 
32,  34;  and  Proof,  17,  31,  68 
note,  94,  97,  214,  217,  227,  347, 
352;    immediate,  95,   208;    de- 


370 


INDEX. 


pendence  on  deduction,  216} 
fallacies  of,  1 77. 

Inquiry,  Btifling  of,  154. 

Instance,  contradictory,  250,  69, 
271,  275,  283 ;  crucial,  235  note. 

Intention  of  speaker,  16,  65,  69, 
70. 

Interpretation,  and  Logic,  16,  21, 
183;  and  counter-indication,  89; 
of  Principle,  103,  109.  See  also 
Meaning  and  Misinterpretation. 

Interval  between  self -contradic- 
tory assertions,  130. 

Invariable  succession,  356,  80. 

Irrelevant  Eeason.  See  Ignoratio 
elenchi. 


Jevons,  Professor,  91,  92, 183,  277, 
309,  349. 

Joint  method  of  Agreement  and 
Difference,  344,  357. 

Judgment,  and  Thesis,  41,  97; 
degrees  of  completeness  in,  41, 
97,  325;  presumption  involved 
in,  162;  reservation  of,  150. 
See  also  Belief,  and  Proposition. 


K 

Keynes,  96. 

Knowledge,  growth  of,  75,  212, 
258;  need  for  special,  in  judg- 
ing evidence,  22,  25,  26,  310; 
generality  of,  76.  See  also  Be- 
lief, and  Proof. 


It. 

Language,  and  Grammar,  4,  64,  66, 
69,  73,  97,  183;  Logic  limited 
by,  45,  47,  132,  187,  321; 
assumptions  required  for,  13, 
46,  106,  134 ;  difficulties  of,  133, 
136,   189,   259,   264;  snares  of, 


174,  176,  186;  and  hidden  differ- 
ence, 258. 
Law,  in  Nature,  14,  71,  81, 285, 272, 
302 ;  and  Fact,  66,  61,  224,  219, 
215 ;  and  explanation,  74 ;  and 
counteraction,  82,  270,  342,  358; 
and  contradictory  instance,  249, 
275,  283,  69,  271;  empirical, 
285,  286,  357 :  chance  and  ten- 
dency, 81,  268 ;  reference  to  in 
concrete  propositions,  76;  re- 
quired   for    all    rationalisation, 

111,  213,  255.  See  also  Principle, 
Generalisation,  Abstract  pro- 
position. 

Laws  of  Thought.  See  Axioms  of 
Consistency. 

Line  of  division,  133,  39,  93,  108, 
124. 

Logic,  and  Philosophy,  2, 3, 12,  46, 
142,  313,  323 ;  and  Common 
Sense,  2,  4,  5,  77,  98,  160,  169, 
317,  321,  323;  and  Physical 
Science,  2,  3 ;  and  Grammar,  15, 
57,  65,  73,  183,  221,  223;  and 
Rhetoric,  15,  8,  23,  180,  200, 
259,  263;  and  Psychology,  14, 
22,  41,  97,  120 ;  and  Scepticism, 
20,  284,  314,  326,  128 ;  and  im- 
plication, 21,  25,  107;  practical 
purpose  of,  2,  3,  6,  8,  10,  13,  17, 

112,  117,  276,  326,  331 ;  disputed 
points  of,  7,  8,  11 ;  clumsiness 
of,  9,  320;  negative  character 
of,  19,  327;  pons  asinorum  of, 
84,  303 ;  province  of,  12 ;  limita- 
tions of,  10,  13,  25,  26,  38,  102, 
117  ;  objections  to,  7,  314 ;  in- 
ductive and  deductive,  19,  110 
note,  212,  276,  330;  logical 
dependence,  63 ;  logical  out- 
come, 103 ;  logical  necessity,  207. 


M. 

MacColl,  H.,  60,  84, 101. 
Margin,  doubtful,  in  names,  134. 
Material  obverse,  89. 


INDEX. 


371 


Maxims  of  Consistency.  See 
Axioms. 

Meaning,  laws  of  interpretation, 
21 ;  agreement  postulated  as 
starting-point,  16,  57,  65 ;  and 
indication,  60,  63,  107 ;  and 
ga,thered  associations,  184,  191, 
199 ;  and  definition,  39, 107, 141, 
385  note;  best,  usual,  and 
special,  of  a  name,  125,  127, 
137;  part  forgotten,  126,  292; 
gradual  change  in,  184,  189 ;  re- 
lative to  standard,  191 ;  of  Thesis 
contained  in  Reason,  26,  204 ; 
meaningless  term,  fallacy  of,  47, 
138 ;  meaningless  questions,  45, 
46,  47,  131,  185  note. 

Mediate  inference,  95,  208. 

Metaphor,  as  argument,  179,  259, 
265 ;  in  names,  189 ;  change  of, 
261 ;  difference  from  analogy, 
198  note,  259;  inclination  to- 
wards, 257,  259,  265. 

Metaphysics.     See  Philosophy. 

Middle  term,  222,  229,  234,  239, 
244,  290,  304,  305 ;  as  sign,  234, 
239;  undistributed,  173,  222. 

Mill,  J.  S.,  15,  19,  53,  107,  170, 
172,  174,  177,  230,  274,  277,  310, 
339,  341,  342,  344,  345, 347,  348. 

Miracles,  157. 

Misinterpretation,  182,  169,  173; 
by  opponent,  188;  and  law  of 
Excluded  Middle,  185;  of 
motives,  171,  175 ;  accusation 
of,  183 ;  avoidance  of,  186.  See 
also  Meaning,  and  Interpreta- 
tion. 

Modi  ponens,  tollens,  etc.,  240,  241. 

Moods  of  Syllogism,  223,  240,  355. 

Mysteiy,  beUef  in,  48,  100,  315. 

N. 

Names,  twofold  use  of,  107  ;  as 
labels,  109,  245;  loose  applica- 
tion of ,  83,  124,  133,  184,  189; 
question-begging,      198,      264 ; 


negative,  65,  71,  93  note ; 
gathered  associations  of,  184, 
191,  199 ;  ancestors'  mistakes  in 
applying,  187.  See  also  Mean- 
ing and  Metaphor. 

Nameable  things,  13,  53. 

Nature,  continuity  of,  133,  336, 14; 
explanation  of,  302,  272,  13; 
natural  laws,  14,  61,  71,  81,  285, 
272,  302. 

Necessary  truth,  207. 

Needs  of  Practice,  4,  13,  20,  38, 
154,  162,  169,  331,  336. 

Negation,  in  propositions,  64,  68, 
223,  243 ;  in  names,  65,  71,  93 
note. 

Negative,  proof  of,  250,  346. 

Newman,  Cardinal,  66,  296. 

Non  Sequitur,  168,  179. 

Nota  NotoB,  245,  301. 

Number  of  confirmatory  facts,  279, 
281,  343. 

.      0. 

Objections,  to  an  assertion,  24;  to 
an  argument,  178 ;  to  Logic,  7, 
314. 

Observation.  See  Experimental 
Methods. 

Obstruction,  of  argument,  50,  128, 
167. 

Obverse,  material,  89. 

Opinion,  prevailing,  159;  and  be- 
lief, 162,  151,  98,  325. 

Opponent,  misinterpretation  by, 
188. 

Opposite,  inconceivability  of,  285. 

Over-generalisation,  177,  256,  270, 
293. 


P. 

Paradox,  45,  130. 

Parallel  cases,  104,  110,  219,  226, 

233. 
Paralogism,  173. 
Particular  propositions,  63. 


372 


INDEX. 


Fetitio  Principii  193,  177,  181 
note,  195,  198,  206,  260,  264; 
and  deduction,  194;  and  tauto- 
logy, 120;  in  names,  198,  264. 

Philology,  and  unsuspected  difEer- 
ence,  258. 

Philosophy,  and  Logic,  46,  2, 3, 12, 
14,  142,  213,  323. 

Platitude,  120,  198. 

Plurality  of  causes,  80,  270,  342, 
351. 

Point  at  i  ssue.  See  Ignoratio  Elenchi. 

Points,  of  difference,  69,  228,  246 ; 
distinction  by,  246,  241 ;  of  re- 
semblance, 228,  253,  300. 

Pons  asinorum  of  Logic,  84,  303. 

Positive  assertion.  See  AflBrmation. 

Post  hoc,  fallacy,  270,  346,  352. 

Postulates.    See  Assumptions. 

Practical  certainty,  38,  94,  205, 
308. 

Practice,  needs  of,  4,  13,  20,  38, 
154,  162,  169,  331,  336. 

Precautions,  in  experiment,  277, 
309,  352. 

Predicate,  54. 

Predication-view  of  propositions, 
53,  54,  231. 

Prediction,  and  explanation,  13,  74, 
219,  272,  302;  predictive  pro- 
positions, 83. 

Premisses,  32,  100;  major  and 
minor,  113,  173,  300. 

Presence  and  absence,  specially 
defined,  85. 

Presumption,  fair,  158,  94;  in- 
volved in  all  judgment,  162  ;  of 
weakness,  165;  raising  of,  209, 
263. 

Prevailing  opinion,  159. 

Principle,  as  reqiiired  for  Proof, 
111,  113,  204,  208,  213,  287,  309, 
329 ;  interpretation  of,  103,  109 ; 
formation  of,  104;  extent  of, 
304,  309,  329;  in  inductive  proof, 
213,  214,  226,  267,  309;  in 
deductive  proof,  213,  245,  287, 
288,  290. 

Probability,  274,  133,  351. 


Proof,  in  general,  99,  97,  111,  113, 

214,  329 ;  meaning  and  aims  of, 
31 ;  etymological  meaning  of, 
36 ;  subject-matter  of,  41 ;  and 
testing,  35;  and  explanation, 
111;  and  resistance  to  attack, 
37  J  and  inference,  17,  31,  68 
note,  97,  214,  217,  347,  352 ;  and 
disproof,  113,  151, 165,  250,  275, 
279;  and  principle.  111,  113, 
204,  208,  213,  287,  309,  329; 
degrees  of,  40,  308,  311,  328; 
unavoidable  incompleteness  of, 
38,  40;  need  for,  143,  42,  149, 
165;  demand  for,  165;  conclu- 
sive, 220,  40,  114,  207,  275,  285, 
300,  328;  empirical  and  deduc- 
tive, 111,  113,  204,  212, 213,  214, 

215,  217,  272,  300;  circum- 
stantial,  221,  224 ;  by  sign,  244 ; 
real,  and  demonstration,  203 ;  of 
axioms,  343  note,  349 ;  of  nega- 
tive, 250,  346;  concerned  with 
complete  assertion  only,  41 ;  ex- 
cuses for  absence  of,  166 ;  often 
not  demanded,  50,  165. 

Propositions,  Subject,  Predicate, 
and  Copula  of,  51 ;  four  views  of 
the  import  of,  53 ;  best  excuse 
for  predication- view,  54 ;  start- 
ing-point and  goal  of,  54,  55 ; 
real  and  unreal,  41 ;  unreal  and 
verbal,  42 ;  apparently  unreal, 
48;  tautologous,  essential  or 
identical,  43;  synthetical  and 
analytical,  42  note ;  self -contra- 
dictory, 44;  simple  and  complex, 
56;  argument  as  complex  pro- 
position, 100, 58, 64,310;  affirma- 
tive and  negative,  64;  abstract 
and  concrete,  66;  abstract-con- 
crete, 77,  276;  notional  and 
real,  66  note  ;  exceptive  denial, 
and  assertion  of  difEerence,  68 ; 
particular,  68;  categorical  and 
hypothetical,  73,  67 ;  of  succes- 
sion, 79 ;  naming,  classifying,  or 
descriptive,  54,  79,  83 ;  explana- 
tory, 83,  123,  219;   predictive, 


INDEX. 


373 


83 ;  reciprocal,  89,  88 ;  disjunc- 
tive, 92. 

Proverbs,  employment  of,  26G. 

Province  of  Logic,  12. 

Provisional  beliefs,  94,  164,  316. 

Psychology,  and  Logic,  14,  22,  41, 
97.  120. 


Q. 

Question-begging.       See      Petitio 

principii. 
Questions,  meaningless,  45,  46,  47, 

131,  185  note ;  verbal,  144. 


Eationalisation,  of  thesis.  111,  213, 
255,  288,  307. 

Eead,  Carveth,  53,  80,  342. 

Eeality,  in  propositions,  41,  42, 
204,  214;  degrees  of,  146. 

Reason  given,  and  Thesis,  relation 
between,  99,  26,  204,  211,  244, 
288,  300,  310,  329;  material 
truth  of,  25,  26, 101, 195 ;  formal 
adequacy  of,  26,  102,  111,  300 ; 
real  and  verbal,  204;  reasons 
and  causes  of  belief,  33. 

Reasoning,  and  rationalisation, 
111,  213,  255,  288,  307;  guidance 
of,  17  ;  direct  and  reflective,  18, 
31 ;  chain  of,  210 ;  gaps  in,  114, 
210,  310,  311,  326. 

Reciprocal  proposition,  89  and 
note,  88 ;  acceptance  as  equiva- 
lent, 91,  173,  288,  290. 

Reductio  ad  absurdum,  298,  174, 
251,  286,  307,  326,  328. 

Reflective  reasoning,  18,  31. 

Relation-view  of  propositions,  53. 

Relevancy  of  Reason,  101,  111,  182, 
191.     See  also  Ignoratio  Elenchi, 

Relevant  fact  overlooked,  181,  252, 
278. 

Resemblance,  striking,  227,  256, 
261 ;  essential,  229,  64,  253,  251, 


266;  neglect  of,  108,  257,  293; 

indistinct,  226;  points  of,  228, 

253,   300;  degrees   of,   227;  of 

circumstances,  272. 
Reservation  of  judgment,  150. 
Residues,  Method  of,  347, 339, 352 ; 

disproof  by,  348. 
Resistance  to  attack,  37,  38,  249, 

273. 
Rhetoric,  15,  8,  23,  180,  200,  259, 

263. 
Rival  theories.     See  Alternative. 
Robertson,   Professor    Croom,   84 

note. 


S. 


Scepticism,  20,  128,  285,  314,  315, 
326 ;  as  an  artifice,  153,  326. 

Science,  physical,  and  Logic,  2,  3. 

Self-contradiction,  103,  129,  44, 
317,  328 ;  contrasted  with  tan. 
tology,  129,  130;  and  epigram, 
129,  45,  132;  requires  dilution, 
to  be  dangerous,  130;  interval 
between  contradictory  asser- 
tions,  131 ;  in  form  of  question, 
131 ;  opposite  causes  of,  132 ;  and 
difiiculties  of  language  (^sorites), 
133 ;  verbal,  not  real,  139,  140. 

Self-deception,  284,  319. 

Self-evident  truths,  46,  149,  207, 
285. 

Senses,  deception  of,  207. 

Sequence.  See  Dependence,  Suc- 
cession, and  Causation. 

Sign,  and  indication,  62,  74,  79, 
90,  107, 113,  239,  245,  301 ;  and 
symptom,  63,  79,  270,  308 ;  and 
naming,  109;  and  middle  term, 
234,  239;  by  presence  and 
absence,  80 ;  a  special  sense  of 
the  name,  79 ;  argument  by,  239, 
220,  286 ;  proof  by,  244,  240. 

Similarity.     See  Resemblance. 

Simplex  enumeratio,  270,  352. 

Simpliciter  et  secundum  quid,  293, 
294. 


374 


INDEX. 


Sole  cause,  269,  834. 

Sorites,  fallacy,  133. 

Special  circumstances,  influence 
of,  67,  68,  72,  282. 

Special  knowledge,  required  in 
judging  evidence,  22, 25,  26,  310. 

Species,  255. 

Spencer,  H.,  20,  47,  53,  130,  190, 
156. 

Starting-point  of  an  assertion,  54. 

Stephen,  Sir  Jas.,  150,  159. 

Subject,  of  a  proposition,  pro- 
yisionally  defined,  42 ;  and 
"  things,"  51 ;  two  in  a  proposi- 
tion, 52. 

Substitution  of  Similars,  349  note. 

Succession,  and  co-existence,  78, 
96,  278  note,  281,  325,  337 ;  in- 
variable, 356,  80 ;  immediacy  of, 
281;  incomplete  indication  of, 
79. 

Suggestive  assertion,  162, 188, 151, 
227,  259,  252,  325. 

Sully,  J.,  14,  181. 

Sunimum  genus,  141. 

Superficiality  of  view,  201. 

Syllogism,  uses  of,  114,  181  note, 
289,  300,  304;  Axiom  of,  301.; 
moods  of,  223,  240,  355;  and 
proof,  111,  113,  212,  204,  207, 
254, 300 ;  syllogistic  fallacy,  209, 
288,  289. 

Symbols,  danger  of,  91,  96 ;  need 
of,  322,  327;  explanation  of 
those  here  employed : — S,  51 ; 
J,  51;  &,  54;  -^,  62;  +>,  68; 
/v,  68;  TandR,  99. 

Synthesis,  259;  synthetical  pro- 
position, 42  note. 


T. 

Tautology,  120, 43,  204;  causes  of, 
121;  resemblance  to  Petitio 
principii,  120;  chief  forms  of, 
123 ;  harmless  when  used  as 
Postulate,  122 ;  finer  shades  of, 
124 ;  Bain's  view  of  verbal  pre- 


dication, 125 ;  dependency  on  ex- 
tent  of  remembrance  of  mean- 
ing, 126,  292 ;  remedy  for,  127  ; 
contrast  with  self-contradiction, 
129,  130. 

Tendency,  81,  268. 

Tentative  assertion.  See  Sugges- 
tive. 

Terms,  51,  and  see  Names  ;  mean- 
ingless, 138,  47;  abstract  and 
concrete,  72. 

Test.     See  Proof  and  Exception. 

Testimony,  221,  225. 

Theory,  219,  252,  271;  and  fact, 
76,  157,  161,  213,  326,  207,  225, 
279 ;  and  axiom,  207,  285 ;  alter- 
native theories,  39,  40, 164,  177, 
239,  270,  275,  276,  310,  311, 328, 
333. 

Thesis,  defined,  18,  41 ;  and  con- 
clusion, 18, 150 ;  and  suggestion, 
122,  325 ;  and  judgment,  41,  97  ; 
and  Reason  combined,  26,  27, 
99,  114,  288,  300;  indicated  by 
Reason,  99,  204,  211,  244,  310, 
329. 

'  Things,'  13,  51,  52. 

Truth,  accepted,  26,  102,  205; 
necessary,  207 ;  self-evident,  46, 
149,  207,  285;  material,  of 
Reason,  25,  26,  101,  195. 

Tyndall,  Professor,  158. 

Types  of  argument,  202. 


U. 

Ultimate  questions,  our  neglect  of, 
46,  3,  12,  142,  171. 

Unbelief  and  disbelief,  326, 154. 

Unconditionality,  358. 

Undistributed  Middle,  173,  222. 

Uniformity,  14 ;  and  see  Law. 

Universe  of  discourse,  93  note. 

Universal.  See  Abstract  proposi- 
tion. 

Unknown  Antecedents,  danger  of, 
in  induction,  270,  279,  284,  349, 
351. 


INDEX. 


375 


Unreal  propositions,  defined,  42; 
remedy  for,  119,  127,  134  j 
degrees  of  unreality,  146. 

Unsupported  assertion,  147,  326. 

Untruth  implied,  178, 179,  300. 


V. 

Vagueness  of  assertion,   49,  187, 

251. 
Variations,   Concomitant,   Method 

of,  348,  339,  343,  352. 
Venn,  J.,  53,  68,  158,  274,  312. 


Vera  Causa,  238,  347,  348, 
Verbal     propositions,     42,     125; 
verbal  ambiguity,  124,  133,  177, 
184,  189 ;  verbal  questions,  144. 
Verifiability  and  reality,  147. 


W. 

Whately,  Archbishop,  18,  31,  144, 
150,  154,  160,  170, 174, 195, 196, 
263. 

Wundt,  Professor,  60,  63,  90t 


THE  END. 


Scientific  Publications. 


MAIf  BIJFOBE  B£ETAI.S.  By  N.  Jolt,  Professor  at  the  Science  Faculty 
of  Toulouse ;  Correspondent  of  the  Institate.  With  148  lUostrations.  12ino. 
Cloth,  11.75. 

"  The  discussion  of  man's  origin  and  early  history,  by  Professor  De  Quatrefages, 
formed  one  of  the  most  useful  volumes  in  the  '  International  ^scientific  iSeries,'  and 
the  same  collection  is  now  further  enriched  by  a  popular  treatise  on  paleontology,  by 
M.  N.  Joly,  Professor  in  the  University  of  Toulouse.  The  title  of  the  book,  •  Man 
before  Metals,'  indicates  the  limitations  of  the  writer's  theme.  His  object  is  to  bring 
together  the  numerous  proofs,  collected  by  modem  research,  of  the  great  age  of  the 
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tant object  is  that  of  considering  the  facts  of  animal  intelligence  in  their  relation  to  the 
theory  of  descent." — From  the  Preface. 

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real  boon  to  the  student  of  Comparative  Psychology  for  this  is  the  first  attempt  to 
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ANTS,  BE£S,  AND  WASPS.  A  Kecord  of  Observations  on  the  Habits  of  the 
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gagements, a  remarkable  illustration  of  economy  of  time.  As  a  contribution  to  insect 
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scientific  spirit  of  the  author,  command  admiration." — New  York  Christian  Advocate. 

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origin  and  development  of  the  myth.  Ihe  author  has  pursued  his  inquiry  with  much 
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"It  is  a  curious  if  not  startling  contribution  both  to  psychology  and  to  the  early 
history  of  man's  development." — New  York  World. 


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THE  CONCEPTS  AND  THEORIES  OF  MODERN  PHYSICS.    By 

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conception,  such  as  the  atomic  constitution  of  matter,  the  kinetic  theory  of  gases, 
the  conservation  of  energy,  the  nebular  hypothesis,  and  other  views,  to  find  how 
much  stands  upon  solid  empirical  ground,  and  how  much  rests  upon  metaphys- 
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no  book  has  been  published  in  the  country  calculated  to  make  so  deep  an  Impres- 
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sinsrular  precision  and  clearness  of  his  style,  are  qualities  which  very  seldom 
have  been  jointly  exhibited  m  a  scientific  treatise." — New  York  Sun. 

THE  FORMATION  OF  VEGETABLE  MOULD,  THROUGH  THE 
ACTION  OF  WORMS,  WITH  OBSERVATIONS  ON  THEIR 
HABITS.  By  Charles  Darwin,  LL.  D.,  F.R.  S.,  author  of  "On  the 
Origin  of  Species,"  etc.,  etc.  With  Illustrations.  12mo,  cloth.  Price,  $1.50. 

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of  observation,  unfailing  power  of  interpreting  and  correlating  facts,  and  logical 
vigor  in  generalizing  npon  them.  The  main  purpose  of  the  work  is  to  point  out 
the  share  which  worms  have  taken  in  the  formation  of  the  layer  of  vegetable 
mould  which  covers  the  whole  surface  of  the  land  in  every  moderately  humid 
country.  All  lovers  of  nature  will  unite  in  thanking  Mr.  Darwin  for  the  new  and 
interesting  light  he  has  thrown  upon  a  subject  so  long  overlooked,  yet  so  full  of 
interest  and  instruction,  as  the  structure  and  the  labors  of  the  earth-worm." — 
Saturday  Review. 

"  Respecting  worms  as  among  the  most  useful  portions  of  animate  nature. 
Dr.  Darwin  relates,  in  this  remarkable  book,  their  structure  and  habits,  the  part 
they  have  played  in  the  burial  of  ancient  buildings  and  the  denudation  of  the 
land,  in  the  disintegration  of  rocks,  the  preparation  of  soil  for  the  growth  of 
plants,  and  in  the  natural  history  of  the  world."— ^o»to»  Advertiser. 

D.  APPLETON  &  CO.,  Publishers, 

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Scientific  Publications. 


SUICIDE  :  An  Essay  in  Comparative  Moral  Statistics.  By  Henet  Mobselli,  Pro< 
feasor  of  Psychological  Medicine  in  Royal  University,  Tiirin.  12Tno,  Cloth,  $l.t5. 
"  Suicide  "  is  a  scientiflc  inquiry,  on  the  basis  of  the  statistical  method.  Into  the  laws 
of  suicidal  phenomena.  Dealing  with  the  subject  as  a  branch  of  social  science,  it  con- 
siders the  increase  of  suicide  in  different  countries,  and  the  comparison  of  nations, 
races,  and  periods  in  its  manifestation.  The  influences  of  age,  sex,  constitution,  cli- 
mate, season,  occupation,  religion,  prevailing  ideas,  the  elements  of  character,  and  the 
.tendencies  of  civilization,  are  comprehensively  analyzed  in  their  bearing  upon  the  pro- 
pensity to  self-destruction.  Professor  Morselli  is  an  eminent  European  authority  on 
this  subject.  It  is  accompanied  by  colored  maps  illustrating  pictorially  the  results  of 
statistical  inquiries. 

VOLCANOES  :  What  they  Are  and  what  they  Teach.  By  J.  W.  Jtod, 
Professor  of  Geology  in  the  Eoyal  School  of  Mines  (London).  With  Ninety -six 
Illustrations.    12mo.    Cloth,  $2.00. 

"  In  no  field  has  modern  research  been  more  fruitful  than  in  that  of  which  Professor 
Judd  gives  a  popular  account  in  the  present  volume.  The  great  lines  of  dynamical, 
geological,  and  meteorological  inquiry  converge  upon  the  grand  problem  of  the  interior 
constitution  of  the  earth,  and  the  vast  influence  of  subterranean  agencies.  .  .  .  KIs 
book  is  very  far  from  being  a  mere  diy  description  of  volcanoes  and  their  eruptions  ;  it 
is  rather  a  presentation  of  the  terrestrial  facts  and  laws  with  which  volcanic  phenomena 
are  associated." — Popular  Science  Monthly. 

"  The  volume  before  us  is  one  of  the  pleasantest  science  manuals  we  have  read  for 
gome  time." — Athenceum. 

"  Mr.  Judd's  summary  Is  so  full  and  so  concise  that  it  is  almost  impossible  to  give 
a  fair  idea  in  a  short  review." — Poll  Mall  Gazette. 

THE  SUN.  By  C.  A.  TotrNG,  Ph.  D.  LL.  D.,  Professor  of  Astronomy  in  the  College 
of  New  Jersey.     With  numerous  Illustrations.    12mo.    Cloth,  $2.00. 

"  Professor  Young  is  an  authority  on  '  The  Sun,'  and  writes  from  intimate  knowl- 
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ments for  observing  it,  gone  to  all  quarters  of  the  world  in  search  of  the  best  places 
and  opportunities  to  watch  it,  and  has  contributed  important  discoveries  that  have 
extended  our  knowledge  of  it. 

"  It  would  take  a  cyclopaedia  to  represent  all  that  has  been  done  toward  clearing  up 
the  solar  mysteries.  Professor  Young  has  summarized  the  information,  and  presented 
it  in  a  form  completely  available  for  general  readers.  There  is  no  rhetoric  in  his  book ; 
he  trusts  the  grandeur  of  his  theme  to  kindle  interest  and  impress  the  feelings.  His 
statements  are  plain,  direct,  clear,  and  condensed,  though  ample  enough  for  his  purpose, 
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yageR."— Popular  Science  Monthly. 

ILiLiUSIONS  :  A  Psychological  Study.  By  Jahes  Sully,  author  of  "  Sensa- 
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This  volume  takes  a  wide  survey  of  the  field  of  error,  embracing  in  its  view  not  only 
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tions, but  also  other  illusions  arising  from  Miat  capacity  for  error  which  belongs  essen- 
tially to  rational  human  nature.  The  author  has  endeavored  to  keep  to  a  strictly  scien- 
tific treatment — that  is  to  say,  the  description  and  classification  of  acknowledged  errors, 
and  the  exposition  of  them  by  a  reference  to  their  psychical  and  physical  conditions; 

"  This  is  not  a  technical  work,  but  one  of  wide  popular  interest,  in  the  principles  and 
results  of  which  every  one  is  concerned.  The  illusions  of  perception  of  the  senses  and 
of  dreams  are  first  considered,  and  then  the  author  passes  to  the  illusions  of  introspec- 
tion, errors  of  insight,  illusions  of  memory,  and  illusions  of  belief.  The  work  is  a  note- 
worthy contribution  to  the  original  progress  of  thought,  and  may  b3  relied  upon  as 
fepresenting  the  present  state  of  knowledge  on  the  important  subject  to  which  it  is 
devoted."~/'o/jM/ar  Science  Monthly. 

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0£N£BAL  PHYSIOI-OGY  OF  MUSCI.ES  AND  NERVES.    By  Dr.  I. 

Rosenthal,  Professor  of  Physiology  at  the  University  of  Erlangen.  With 
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$1.50. 

"  The  attempt  at  a  connected  account  of  the  general  physiology  of  muscles 
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'branch  of  Bcience  have  been  gained  only  within  the  past  tliirty  years."— .Kef rac< 
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SIGHT :  An  Exposition  of  the  Principles  of  Monocular  and  Binocular  Vision. 
By  Joseph  Le  Conte,  LL. D.,  author  of  "Elements  of  Geology";  "Re- 
ligion and  Science  " ;  and  Professor  of  Geology  and  Natural  History  in  the 
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"  It  is  pleasant  to  find  an  American  book  which  can  rank  with  the  very  best 
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an  orii;inal  investigator  in  this  department;  all  that  he  gives  ns  is  treated  with 
a  master-hand."— rAe  Nation. 

ANIMAIi  ULFE,  as  affected  by  the  Natural  Conditions  of  Existence.  By 
Karl  Semper,  Professor  of  the  University  of  W^lirzburg.  With  2  Maps 
and  106  Woodcuts,  and  Index.    12mo,  cloth,  $2.00. 

"This  is  in  many  respects  one  of  the  most  interesting  contributions  to 
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THE  ATOMIC  THEORY.  By  Ad.  Wubtz,  Membre  de  I'lnstitut ;  Doyen 
Honoraire  de  la  Faculte  de  Medecine ;  Professeur  a  la  Paculte  des  Sciences 
de  Paris.  Translated  by  E.  Cleminshaw,  M.  A.,  F.  C.  S.,  F.  I.  C,  Assist- 
ant Master  at  Sherborne  School.    12mo,  cloth,  $1.50. 

"  There  was  need  for  a  book  like  this,  which  discusses  the  atomic  theory  both 
in  its  historic  evolution  and  in  its  present  form.  And  perhaps  no  man  of  this 
age  could  have  been  selected  so  able  to  perform  the  task  in  a  masterly  way  as 
the  illustrious  French  chemist.  Adolph  Wnrtz.  It  is  impossible  to  convey  to  the 
reader,  in  a  notice  like  this,  any  adequate  idea  of  the  scope,  lucid  instructiveness, 
and  scientific  interest  of  Professor  Wnrtz' s  book.  The  modern  problems  of 
chemistry,  which  are  commonly  so  obscure  from  imperfect  exposition,  are  here 
made  wonderfully  clear  and  attractive." — The  Popular  Science  Monthly. 

THE  CRAYFISH.  An  Introduction  to  the  Study  of  ZoOlogy.  By  Professor 
T.  H.  Huxley,  F.  B.  8.    With  82  Illustrations.    12mo,  cloth,  $1.75. 

"  Whoever  will  follow  these  pages,  crayfish  in  hand,  and  will  try  to  verify  for 
himself  the  statements  which  they  contain,  will  find  himself  brought  face  to  face 
with  all  the  irreat  zoological  questions  which  excite  so  lively  an  interest  at  the 
present  day." 

'•  The  reader  of  this  valuable  monograph  will  lay  it  down  with  a  feeling  of 
wonder  at  the  amount  and  variety  of  matter  which  has  been  got  out  of  so  seem- 
ingly slight  and  unpretending  a  aaVinct."— Saturday  Beview. 

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THE  HUMAN  SPECIES.  By  A.  De  Quatbefages,  Professor  of  Anthro- 
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The  work  treats  of  the  unity,  origin,  antiquity,  and  original  localization  of 
the  human  species,  peopling  of  the  globe,  acclimatization,  primitive  man,  forma- 
tion of  the  human  races,  fossil  human  races,  present  human  races,  and  the  physi- 
'cal  and  psychological  characters  of  mankind. 

STUDENTS'  TEXT-BOOK  OP  COtOR ;  or,  MODERN  CHROMAT- 
ICS. With  Applications  to  Art  and  Industry.  With  130  Original  Illus- 
trations, and  Frontispiece  in  Colors.  By  Ogden  N,  Eood,  Professor  of 
Physics  in  Columbia  College.    12mo,  cloth,  $2.00. 

"In  this  interesting  book  Professor  Rood,  who,  as  a  distinguished  Professor 
of  Physics  in  Columbia  College,  United  States,  must  be  accepted  as  a  competent 
authority  on  the  branch  of  science  of  which  he  treats,  deals  briefly  and  succinctly 
with  what  may  be  teimed  the  scientific  rationale  of  his  subject.  But  the  chief 
value  of  his  work  is  to  be  attributed  to  the  fact  that  he  is  himself  an  accom- 
plished artist  as  well  as  an  authoritative  expounder  of  science."— ^ainftwr^A 
Eeview,  October,  1879,  in  an  article  on  "  The  Philosophy  of  Color" 

EDUCATION  AS  A  SCIENCE.  By  Alexander  Baik,  LL.  D.  18mo,  cloth, 
$1.75. 

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bespeak  for  it  the  widest  circulation  and  the  most  earnest  attention.  It  should 
be  in  the  hands  of  every  school-teacher  and  friend  of  education  throughout  the 
land."— JVew  York  Sun. 

A.  HISTORY  OF  THE  GROWTH  OF  THE  STEAM-ENGINE.    By 

Robert  H.  Thurston,  A.  M.,  C.  E.,  Professor  of  Mechanical  Engineering 
in  the  Stevens  Institute  of  Technology,  Hoboken,  N.  J.,  etc.  With  163 
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agree  that  it  could  have  a  no  more  amusing  and  intelligent  historian  than  our 
author."— .Bcwtow  Gazette. 

STUDIES  IN  SPECTRUM  ANAI-TSIS.  By  J.  Norman  Lockteb,  P.  R.  S., 
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Bults.  They  are  so  lucidly  described,  too.  that  the  reader  keeps  on,  from  page 
to  page,  never  flagging  in  interest  in  the  natter  before  him,  nor  putting  down 
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ANTHROPOLOGY :  An  Introduction  to  the  Study  of  Man  and  Civilization. 
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SCIENTIFIC  CUITURE,  AND  OTHER  ESSAYS.  By  Joseph  Parsons 
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POPULAR  LECTURES  ON  SCIENTIFIC  SUBJECTS.  By  H.  Helm- 
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12mo,  cloth,  $1.50. 

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THE  POWER  OF  MOVEMENT  IN  PLANTS.  By  Charles  Darwin, 
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from  him  at  intervals,  never  much  prolonged,  the  results  of  special  research  in 
some  by-path  or  other  subordinated  to  the  main  course  of  the  biological  system 
associated  with  his  name;  and  it  has  been  an  unfailing  source  of  interest  to  see 
the  central  ideas  of  the  evolution  and  the  continuity  of  life  developed  in  detail 
through  a  series  of  special  treatises,  each  weUnigh  exhaustive  of  the  materials 
available  for  its  subject."— (Saiwrday  Beview. 

A  PHYSICAL  TREATISE  ON  ELECTRICITY  AND  MAGNETISM. 

By  J.  E.  H.  Gordon,  B.  A.,  Assistant  Secretary  of  the  British  Association. 
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investigator  and  every  teacher  who  goes  beyond  the  merest  rudiments  must  needs 
equip  himself.  There  is  certainly  no  book  in  English — we  think  there  is  none  in  any 
other  language — which  covers  quite  the  same  ground.  It  records  the  most  recent  ad- 
vances in  the  experimental  treatment  of  electrical  problems,  it  describes  with  minute 
carafiilness  the  instruments  and  methods  in  use  in  physical  laboratories,  and  is  prodi- 
gal of  beautifully  executed  diagrams  and  drawings  made  to  scale." — London  Times. 

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THE  FUNDAMENTAIi  CONCEPTS  OF  MODEKN  PHItOSOPHIO 
THOUGHT,  CKITICALXiY  AND  HISTORlCAL,L,Y  CONSID- 
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self with  the  course  of  modem  speculation  and  scientific  thinking,  and  to  form 
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MIND  IN  THE  tOWEK  ANIMAI-S  IN  HEAI.TH  AND  DISEASE. 

By  W.  Lauder  Lindsay,  M.  D.,  F.  R.  S.  E.,  etc.    2  vols.,  8vo.    Cloth,  $4.00. 

"  The  author  of  this  work,  which,  regarded  merely  as  an  accumulation  of 
verified  and  classified  facts,  is  a  unique  and  precious  contribution  to  the  data  of 
comparative  psychology,  claims  that  he  entered  on  his  inquiry  without  any  tlieory 
to  defend,  support,  or  illustrate.  We  are  bound  to  say  that,  while  his  general 
conclusions  are  boldly  and  continually  avowed,  his  claim  of  fairness  and  caution 
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willing  at  all  times  to  renounce  any  impression  or  belief  which  is  shown  to  be 
Bcientifically  untenable."— iVew  York  Sun. 

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portionately large  number  of  facts  against  those  philosophers  who  maintain  that 
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lower  animals.  It  is  one  purpose  of  his  book  to  show  that  the  main  difierences 
between  man  and  the  lower  animals  exist  rather  in  their  physical  than  in  their 
mental  structure.  In  this  way  of  thinking,  all  animals  possess  not  the  semblance 
of,  but  the  true  substance  of  mind  and  will." — JVew  York  World. 

"  So  far  as  we  are  aware  there  has  been  no  treatise  upon  the  subject  of  animal 
intelligence  so  broad  in  its  foundations,  so  well  considered,  or  so  scientific  in  its 
methods  of  inquiry,  as  that  which  has  been  prepared  by  Dr.  W.  Lauder  Lindsay 
in  two  large  volumes,  the  first  being  devoted  to  a  study  of  animal  mind  in  health, 
and  the  second  to  animal  mind  in  disease.  We  may  safely  say  that  his  work  is, 
in  some  respects,  the  most  important  essay  of  the  kind  that  has  yet  been  under- 
taken. His  observations  have  been  supplemented  by  a  thorough  mastery  of  the 
history  and  literature  of  the  subject,  and  hence  his  conclusions  rest  upon  the 
broadest  possible  foundation  of  safe  induction.  There  is  a  good  analytical  index 
to  the  book,  as  there  ought  to  be  to  every  work  of  the  kind." — New  York  Evening 
Post. 

THE  ELEMENTARY  PRINCIPI-ES  OF  SCIENTIFIC  AGRICULT- 
URE. By  N.  T.  LuPTOK,  LL.  D.,  Professor  of  Chemistry  in  Vanderbilt 
University,  Nashville,  Tenn.    18mo.    Cloth.    Price,  45  cents. 

A  GLOSSARY  OF  BIOLOGICAI^  ANATOMICAL,  AND  PHYSIO- 
LOGICAL TERMS.  By  Thomas  Dunman.  Small  8vo.  Cloth.  161 
pages.    Price,  $1.00. 

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complete  glossary  of  those  terms  ;  and  he  has  done  this  so  well,  both  in  his  choice 
of  terms  for  definition  and  in  his  clear  exposition  of  their  etymological  and  tech- 
nical meaning,  as  to  leave  nothing  to  be  desired  in  this  direction." — New  York 
Evening  Post.  

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A  TREATISE    ON  CHEMISTRY.     By  H.  E.  Robcoe,  F.  R.  8.,  ond  C. 

ScuoRLEsiMER,  P.  K.  8.,  ProfeBsors  of  Chemistry  in  the  Victoria  Uuivereity, 
UweDB  College,  Manchester.    IlluBtrated. 

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ment,  or  the  wealth  of  illustrations  which  explain  and  adorn  the  text.  Whatever 
testa  of  accuracy  as  to  figures  and  facts  we  have  been  able  to  apply  have  been 
satisfactorily  met.  while  in  clearness  of  statement  this  third  Tolam& leaves  noth- 
ing to  be  deaired."— London  Academy. 

THE   ELEMENTS  OF  EC0N03IICS.     By  Henbt  Dunning  Macxeod. 
M.  A.,  of  Trinity  College,  Cambricige,  and  the  Inner  Temple,  barrister-at- 
law  selected  by  the  Royal  Commissioners  for  the  Digest  of  the  Law  to  pre- 
pare the  digest  of  the  law  of  bills  of  exchange,  bank  notes,  etc.    Lecturer 
on  Political  Economy  in  the  University  of  Cambridge.     In  two  volumes. 
Volume  I  now  ready.    12mo,  cloth.    Price,  $1.75. 
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to  the  class  of  books  that  assist  inquiry  by  setting  their  readers  thinking.    The 
views  they  set  forth  are  not  only  often  valuable  in  themselves,  but  they  are  the 
generative  cause  of  ideas  which  may  also  be  valuable  in  their  readers.     His 
books,  moreover,  are  written  in  the  proper  way.    The  subject  is  divided  care- 
fully in  accordance  with  the  opinions  held  by  the  author ;  all  classifications  when 
made  are  adhered  to,  and  the  descriptions  and  definitions  adojjted  are  admir.able 
from  his  point  of  view,  and  in  some  cases  from  a  wider  stand-point."— 27ec  Statist. 

ADOIiPH    STRECKER'S    SHORT    TEXT-BOOK    OF    ORGANIC 

CHEMISTRY.    By  Dr.  Johannes  Wislicenus.   Translated  and  edited, 

with  Extensive  Additions,  by  W.  H.  Hodgkinson,  Ph.  D.,  and  A.  J.  Gheen- 

AWAT,  F.  I.  C.    8vo.    Cloth,  $5.00. 

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primer.    Everything  is  comparative,  and  the  term  '  short '  here  has  relation  to 

the  enormous  development  and  extent  of  recent  organic  chemistry.    This  oolid 

and  comprehensive  volume  is  intended  to  represent  the  present  condition  of  the 

science  in  its  main  facts  and  leading  principles,  as  demanded  by  the  systematic 

chemical  student.    We  have  here,  probably,  the  best  extant  text-book  of  organic 

chemistry.    Not  only  is  it  full  and  comprehensive  and  remarkably  clear  and 

methodical,  but  it  is  up  to  the  very  latest  moment,  and  it  has  been,  moreover, 

prepared  in  a  way  to  secure  the  greatest  excellences  in  such  a  treatise." — The 

Popular  Science  Monthly. 

THE  ORIGIN  OF  CIVILIZATION  AND  THE  PRIMITIVE  CON- 
DITION  OF  MAN,  Mental  and   Social    Condition   of  Savages. 

By  Sir  John  Lubbock,  Bart ,  F.  R.  S.,  President  of  the  British  Association. 
With  Illustrations.  Fourth  edition,  with  numerous  Additions.  8vo,  cloth. 
Price,  $5.00.  

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SCIENCE  AND  CUIiTURE,  AND  OTHER  ESSAYS.  By  Professor 
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"  Of  the  essays  that  have  been  collected  by  Professor  Huxley  in  this  volume, 
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expositions  of  the  results  of  biological  research,  and,  at  the  same  time,  illustra- 
tions of  the  history  of  scientific  ideas.  Some  of  these  are  amon^  the  most  inter- 
esting of  Professor  Huxley's  contributions  to  the  literature  of  science." — London 
Academy. 

"  When  weary  of  the  iteration  of  old  thoughts  dressed  up  in  new  phrases,  it 
is  refreshing  to  be  brought  into  converse  with  one  of  the  most  vigorous  and  acute 
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CAPITAIi    AND    POPUIiATION :  A  Study  of  the  Economic  Effects 

of  their   Relations   to  Each  Other.     By  Fbedbrick  B.  Hawlet. 

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on  nearly  all  the  unsolved  problems  of  the  science." — Extract  from  Preface. 

PHYSICAIi    EDUCATION ;    or,  The  Health  Laws  of  Nature.     By 

Felix  L.  Oswald,  M.  D.    12mo.    Cloth,  $1.00. 

Contents:  Diet,  In-door  Life,  Ont-door  Life,  Gymnastics,  Clothing,  Sleep, 
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"  The  author  strikes  right  and  left  at  the  lingering  traces  of  the  traditional 
asceticism  which  has  had  so  much  influence  in  warping  our  systems  of  education 
and  life. .  He  insists,  at  the  outset,  that  the  monkish  identiflcation  of  the  human 
body  with  Satan  and  sin  shall  be  discarded  utterly,  and  that  we  shall  regard  this 
tabernacle  of  clay  as  the  most  perfect  structure  of  the  divine  architect,  and  as  the 
sole  means  by  which  we  can  work  out  our  salvation.  Nature  is  the  author's 
supreme  law,  and  his  cure  for  all  maladies  of  the  individual  and  the  community 
is  right  living." — Home  Journal. 

"  Dr.  Oswald  is  as  epigrammatic  as  Emerson,  as  spicy  as  Montaigne,  and  as 
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THE  PRINCIPLES   OF  THE  LAW :  An  Examination  of  the  I^aw 
of  Personal  Rights,  to  discover  the  Principles  of  the  Iia'w,  aa 
ascertained  from   the   Practical   Rules   of  the   Iiavr,   and  har- 
monized -with  the  Nature  of  Social  Relations.    By  A.  J.  Willabd. 
8vo,  cloth.    Price,  $2.50. 
"  A  calm,  dignified,  able,  and  exhaustive  treatise  of  a  subject  which  is  of  great 
importance  to  every  one.    Mr.  Willard  first  discusses  the  nature  and  origin  of 
rights,  obligations,  and  powers  of  fundamental  social  law  and  institutional  law. 
He  then  expounds  the  science  of  law  and  defines  the  nature  of  all  species  of  obli- 
gations and  contracts.    A  general  view  of  rights  and  powers  is  then  brought 
forward,  and  a  consideration  of  their  special  functions,  as,  for  instance,  the  use 
of  air  and  water  and  the  principles  of  individual  sustenance.     The  doctrine  of 
individual  redress  and  protection  is  thoroughly  examined,  and  a  long  and  inter- 
esting discussion  follows  of  nuisance*!,  wrongs,  and  injuries.    The  characteriza- 
tion of  dueling  and  the  pithy  and  convincing  way  in  which  its  absurdity  is  shown 
are  admirable.    The  treatment  of  the  subject  is  so  clear  and  logical,  so  simple 
and  scholarly,  that  it  deserves  the  highest  praise.    It  is  a  work  such  as  Aristotle 
might  have  written,  had  he  lived  in  this  latter  day." — Philadelphia  Press.  t 

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The  Winners  in  Life's  Race ; 

OB,  THE  GREAT  BACKBOiTED  FAMILY.  With  nu- 
merous Illustrations.     12mo.     Cloth,  gilt,  $1,50. 

Life  and  Her  Children. 

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Fairy-Land  of  Science. 

With  numerous  Illustrations.     12mo.     Cloth,  $1.50. 

"  It  deserves  to  take  a  permanent  place  in  the  literatm-e  of  youth." — 
London  limes. 

"  So  interesting  that,  having  once  opened  the  book,  we  do  not  know 
how  to  leave  off  reading." — Saturday  Review. 

A   Short    History  of  Natural   Science   and   the 
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